1. On the passage:  ”And Abraham lifted up his eyes, and he saw, and lo! there was a ram.. And Abraham went and took the ram and offered it up as a burnt offering instead of his son.” 

Rashi explains: “instead of his son: Since it is written: “and offered it up for a burnt offering,” Nothing is missing in the text. Why then [does it say]: “instead of his son”? Over every sacrificial act that he performed, he prayed, “May it be [Your] will that this should be deemed as if it were being done to my son: as if my son were slaughtered, as if his blood were sprinkled, as if my son were flayed, as if he were burnt and reduced to ashes.” - [from Tan. Shelach 14]”

This needs understanding:

On the previous passage:"Please take your son.. and bring him up there for a burnt offering (22:2)” Rashi explains: “bring him up: He did not say to him, “Slaughter him,” because the Holy One, blessed be He, did not wish him to slaughter him but to bring him up to the mountain, to prepare him for a burnt offering, and as soon as he brought him up [to the mountain], He said to him, “Take him down.” - [from Gen. Rabbah 56:8] and Hashem made known to Abraham afterwards, as mentioned by Rashi on the passage:   “And he said, "Do not stretch forth your hand to the lad, nor do the slightest thing to him, for now I know that you are a G-d fearing man etc (22:12)) That Hashem, said to Avraham (Ps. 89:35): “I shall not profane My covenant, neither shall I alter the utterance of My lips.” When I said to you,” Take,” I was not altering the utterance of My lips. I did not say to you,” Slaughter him,” but,” Bring him up.” You have brought him up; [now] take him down. ” [from Gen. Rabbah 56:8]
 

And since Avraham Avinu already knew that,”Hashem didn’t want to slaughter him  but rather to offer him up” -  until it was impossible to do otherwise because “neither shall I alter the utterance of My lips” , Hashem promised to Avraham Avinu that “With Isaac will be called your seed”-  

We therefore need to understand how Abraham offered the ram “instead of his son”,  and that “he prayed .. (“May it be Your will) as if my son was slaughtered etc”, because Hashem did not want him to be slaughtered?
 

And we can’t answer that since the ram appeared at that time (and especially according to Rashi that the ram ran to Avraham Avinu), that Avraham Avinu understood that HaShem wanted that he should be offered on the altar - because this is a proof that Hashem wanted (the ram) to be offered on the alter but not to innovate (leChadeish) a desire (that for Hashem wanted) to offer it (the ram)  ”instead of his son”

 

And moreover: From  the words of Rashi - that “he prayed .. May it be Your will) that it should be as if  it were done to my son” is understood that Avraham Avinu did this ( the offering the ram “instead of his son”)  not because of the command of HaShem, (or because he understood that this was the will of G-d) but rather this was will (and “innovation”) of Avraham Avinu,  therefore he needed “pray to G-d”  that He should accept this offering “as if were done to my son”.

And the question remains: G-d said to Avrohom “the words of my lips I will not change - I did not tell you to slaughter him but offer him” “ Yet Avraham Avinu wanted and strived to add a sacrifice “instead of his son”!!

2. Some explain that this was in “exchange of what it was in his (Avraham Avinu’s) heart to slaughter his son, like: ”and speaks truth in his heart (Psalms 15:2)” for since “he had decided to complete the action ... he thought he was obligated to give something as an atonement and exchange instead of this”

In other words:  Even though the command of G-d was only to “offer him” and not to “slaughter him”, nevertheless since Avraham Avinu resolved in his heart to slaughter his son, he obligated himself to fulfill what was in his heart (at least though a substitution) - because he “speaks truth in his heart”
 

But it’s difficult to answer this in Rashi’s commentary - because we don’t even find a hint to this answer in Rashi;

On the other hand, this answer isn’t so “simple” as to say that Rashi didn’t need to write it explicitly (because the student would understand it himself) - because one could say the opposite, that in this situation the maxim “speaks truth in his heart” does not apply because since “G-d did not  want him to slaughter him (Isaac)”, there is no reason to say that Avraham Avinu should endeavor to keep his previous thought (resolution) ( even in a manner of “as  if” his son was slaughtered), against the will of G-d.

Therefore, even if one could say that Rashi holds that there is a place for this explanation, he (Rashi) should have written it explicitly ( as explained many times, that Rashi wrote his commentary clearly, alleviating the student from searching for an explanation in  other commentaries to understand his intent)

3. This can be understood by prefacing another question about these verses “ that we do not find that Rashi has answered:

The verses state, that when Avraham Avinu “stretched forth his hand .. to slaughter his son (22:9)   That “an angel of G-d called to him (22:11) and said, "Do not stretch forth your hand to the lad,.. for now I know that you are a G-d fearing man, and you did not withhold your son, your only one, from Me.(22:12)" and after Avraham Avinu saw the ram and “offered it up as a burnt offering instead of his son”, “an angel of the Lord called to Abraham a second time from heaven” and told him "By Myself have I sworn, says the L-rd, that because you have done this thing and you did not withhold your son, your only one,” That I will surely bless you, and I will greatly multiply your seed as the stars of the heavens and as the sand that is on the seashore, and your descendants will inherit the cities of their enemies. (22:15-17).

And it’s not understood (as the commentators ask):

Why did the angel need to call him (Avraham Avinu) a “second time from heaven” to give him all the blessings that he deserved:  ”because you have done this thing and you did not withhold your son, your only one”?
 
Why didn’t he (Angel) tell him all this the first time (calling)?
 

And the understanding of the passages is that, even though Avraham Avinu was blessed with these blessings “because you have done this thing and you did not withhold your son, your only one”. Nevertheless, he wasn’t actually blessed until he offered the ram  -and we need the reason for this.

4.  One can say the explanation is:

The innovation of these blessings: “and I will greatly multiply your seed as the stars of the heavens and as the sand that is on the seashore, and your descendants will inherit the cities of their enemies (22:17)”, even though Avraham Avinu was blessed as such many times before this ( as told in Parshas Lech Lecha),  - is (as explained in the verse) that now Hashem swore on them “ "By Myself have I sworn, says the Lord, that because you have done this thing, that I will surely bless you etc” (for through the oath he was promised that nothing would nullify the blessings to him).

And accordingly, one should not question why Rashi did not explain the reason that the oath came specifically at the “second” calling after the offering of the ram  - because this is understood from the narrative in Chumash (Torah) concerning the first oath of G-d.

In the passages after the Flood it says that:  

“Noah built an altar to the Lord, and he took of all the clean animals and of all the clean fowl and brought up burnt offerings on the altar.(8:20)” “And the L-rd smelled the pleasant aroma, and the L-rd said to Himself, "I will no longer curse the earth because of man,.(8:21)

And Rashi explains: “I will no longer..and I will no longer: He repeated the words to denote an oath. That is what is written (Isa. 54:9): “That I swore that the waters of Noah shall never again pass over the earth,” and we do not find an oath concerning this matter except in this [statement, in] (which He repeated His words, and this [repetition denotes that it] is an oath. So did our Sages expound in Tractate Shevuoth (36a).)

It is clear that G-d’s oath to “no longer” destroy the earth through a flood came as a result of the pleasant aroma of Noach’s burnt offerings.

And the same thing is in our situation: Hashem’s oath on the blessings came through the offering of Avraham Avinu (of the ram). Therefore the oath came only at the “second” calling, after the offering of the ram.

And this is the reason that Avraham Avinu wanted to offer the ram “instead of his son” -  for in order that his offering should effect that, the blessings for the test of the Akeidah (which are critical aspects to the existence of the Jewish people) , would be guaranteed by an oath, required a connection and tie between the offering and the test.

And like we find in the offerings of Noah (that effected the oath that: “I will no longer (destroy)”), For in addition to the fact that offerings came immediately after he came out of the ark (close to the end of the flood) the offerings themselves were animals saved that were saved from the flood.

Also in our case, in order to connect this offering (ram) with the binding of Isaac he offered the ram “instead of his son”.

5. Accordingly, the lengthiness of Rashi’s explanation on the passage of “instead of his son” is understood.   “Over every sacrificial act that he performed, he prayed, “May it be [Your] will that this should be deemed as if it were being done to my son” (And he (Rashi) then specifies all the acts) - as if my son were slaughtered..as if his blood were sprinkled.. as if my son were flayed .., as if he were burnt and reduced to ashes.” “ for this expressly points out the connection between the offering of the ram with the binding of Isaac, for through the offering of the ram “instead of his son”, Avraham Avinu affected that Isaac himself should be on the level of an offering.

In other words, the intent of the passage that the offering of the ram was “instead of his son”, could have been explained, that the offering of the ram was in place of his son. Namely, that through the offering of the ram the status of offering was removed from his son, and rested on the ram.  But Rashi innovates that the explanation of “instead of his son” is the opposite, that through the offering of the ram, it is “as if it was done to my son”, and through it the status of offering is placed on Isaac.   And this “ the placing of the status of an offering on Isaac through the offering of the ram  - was an innovation of Avraham Avinu, therefore he had to pray to Hashem - that “May it be [Your] will that this should be deemed as if it were being done to my son” 

And the explanation is: The intent of Hashem at the Akaidah (Binding) was seemingly only to test Avraham Avinu, (as explained in the verse) he should be completely prepared to offer his only son to Hashem, but not that Isaac actually be offered as an offering. (On the contrary,  ”neither shall I alter the utterance of My lips” therefore He said “bring (offer) him up “but not “slaughter him” because Hashem did not want him to be slaughtered)

But Avraham Avinu who wanted to effect an oath of Hashem (through the “aroma” of the offerings, as above) strove that the status of offering should be on Isaac, in order that the Akeidah should also have the benefit (maalah) of an offering (and through this the blessings on the Akeidah would be promised to him in a manner of an oath): Therefore he offered the ram “instead of his son” and prayed  to HaShem “May it be [Your] will that this should be deemed asif it were being done to my son” 

And accordingly the order of the passages makes sense (yumtak):

"By Myself have I sworn, says the L-rd, that because you have done this thing and you did not withhold your son, your only one (22:16)” for the understanding is that (also) the oath that came after the offering was “because” (yaan)- (the outcome of this) that “you have done this thing” etc   and “and you did not withhold your son, your only one” for (also) through the offering of the ram Avraham Avinu showed that the didn’t spare his only son from HaShem, since he prayed that “that this should be deemed as if it were being done to my son” 

6.  But there is still missing an explanation: It is true that in the story of Noach, the oath of Hashem came through the “aroma” of the offerings (of the animals)” However, in our case, how is it possible to say that the test of the Akaidah itself- where Avraham Avinu revealed that he was ready to offer his only son to HaShem, was not enough to effect the oath of G-d and only the offering of the ram “instead of his son”, did this itself cause the oath of HaShem?

One can say that the explanation is:

Even though at the Akaidah, Avraham Avinu revealed that was that he was prepared to offer his only son to HaShem, nevertheless this did not achieve the exact same status of an offering because it did not result in an actual offering.  Because even after his resolution with a full heart, and all the preparations that he did to offer his son Isaac as an offering, that he “subdued his mercy” to offer him (Isaac) to Hashem- nevertheless since he didn’t “do anything”, and the offering didn’t actually come about, it is not a certain (offering i.e., it is not the same as an actual offering).  And understood simply, subduing of mercy with preparations to “slaughter his son” is not similar to the subduing of mercy that is required at the time of actually doing it.

[and this can be compared to someone who sacrifices his soul (bPoail) in actuality compared to someone who made a resolution (bKoach) to do so (even though he resolved in his mind to be prepared (if the opportunity arises) to sacrifice his soul to HaShem). Because when one is required to actually sacrifice his soul, he has to arouse in his soul strength and extreme powers just to be prepared in his mind, as understood]

Therefore:  Concerning the test of the Akaidah, it was (also) enough the “subduing of his mercy”, with the preparation of Avraham Avinu, For in this he already had proved that “for now I know that you are a G-d fearing man” - Nevertheless, he didn’t have the benefit of an offering, an offering to Hashem (in actuality)

7.  And this is also the reason that when the angel told Avraham Avinu:
 

"Do not stretch forth your hand to the lad” Avraham Avinu said “I will inflict a wound on him and extract a little blood.(Rashi 22:12)”  Seemingly, what is the advantage of letting out a drop of blood, he will not fulfill through this the commandment of “offering him as a burnt offering”?  ”Rather through this he would feel the aspect of sacrificing (his soul) in actuality

Therefore the angel told him:”Do not do the slightest thing to him.” - and Avraham Avinu wanted that the action of the Akaidah should have the benefit of an offering, offered the ram “instead of his son” and “Over every sacrificial act that he performed, he prayed, “May itbe [Your] will that this should be deemed as if it were being done to my son”

When Avraham Avinu slaughtered the ram, he thought and felt in his soul that he is slaughtering Isaac ( so too with all the sacrificial act s  that he did performed with the ram) in a manner that the sacrificing of the ram aroused within him the characteristic of actually “subduing his mercy”, that at the time of slaughtering, he felt in his mind as if he was slaughtering Isaac.

And therefore Avraham Avinu prayed, that through this thought and arousal it should be considered “as if it were being done to my son”  the advantage of actually being an offering

 

And on this, the answer of HaShem came ( through the angel) -"By Myself have I sworn, says the Lord, that because you have done this thing…That I will surely bless you, and I will greatly multiply your seed etc and your descendants will inherit the cities of their enemies.”

For this will be fulfilled (completely “in the future Geulah for us” speedily in our days, really.

(Sichat Vayeira 5737)