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בעצם היום הזה ON THE SELFSAME DAY when Abraham completed his ninety-ninth year and Ishmael his thirteenth year נמול אברהם וישמעאל בנו WAS ABRAHAM CIRCUMCISED AND ISHMAEL HIS SON.

IN THE SELFSAME DAY WAS ABRAHAM CIRCUMCISED. Rashi wrote: “In the selfsame day when Abraham completed his ninety-ninth year and Ishmael his thirteenth, they were circumcised.”
But what reason is there to mention this? Moreover, there is already general agreement with the words of Rabbi Eliezer⁴⁶³Rosh Hashanah 12 a; also ibid., 27a. See also Seder Noach, Note 148, for fuller discussion of this point. who said that in the month of Tishri the world was created, and in Tishri the patriarchs were born, with the exception of Isaac who was born on Passover. Now Scripture says that the birth of Isaac will be at this time in the next year,⁴⁶⁴Verse 21 here. and Rashi himself wrote further on in Seder Vayeira⁴⁶⁵Further, 18:10. that the tidings were given on Passover. Consequently, Isaac was born on the next Passover!⁴⁶⁶How then could Rashi say that on this selfsame day Abraham completed his ninety-ninth year, thus making Passover his birthday, when the consensus of opinion is, as Rabbi Eliezer says, that the patriarchs were born in Tishri?
Instead, the expression, In the selfsame day, means that on the very day he was charged with this commandment, he and the men of his house — three hundred and eighteen⁴⁶⁷Above, 14:14. — and all those purchased with his money were circumcised. Scripture thus tells of Abraham’s distinction with respect to the fear of G-d, as well as that of all the men of his house, i.e., that they were all zealous, fulfilling their religious duty as promptly as possible.
Now the meaning of the phrase, was Abraham circumcised and Ishmael his son, is not that Abraham was circumcised first. Instead, it was Ishmael who was circumcised first, and then all the men of Abraham’s house, for it is so written: And Abraham took Ishmael his son, and all that were born in his house,⁴⁶⁸Verse 23 here. and after that it says, And Abraham was ninety years and nine when he was circumcised.⁴⁶⁹Verse 24 here. The reason for this was that Abraham was zealous concerning the commandment to circumcise them first, either doing it himself or perhaps inviting many circumcisers whom he supervised, and then he circumcised himself. Had he performed his circumcision first, he would have been sick or in danger on account of his advanced age, and he would then not have been in a position to concern himself with their circumcision.
Vayeira

בעצם היום הזה; we (the Torah) have already stated that Avraham circumcised all the members of his household on the very day G'd issued the command to him (verse 23). The Torah had not mentioned that he also circumcised himself and his son on that day. This is why this is added here, to tell us that he brooked no delay in performing the commandment both on his son and on himself. The meaning of the word נימול is that he performed the operation on himself and did not delegate anyone to do it as his agent. The use of a passive mode to describe that someone did something himself is not unique. We find it also in Samuel II 20,10 וכן עמשא לא נשמר, "and so Amassa did not protect himself."

בעצם היום הזה, “on this very day.” According to Rashi the meaning of בעצם היום הזה is: “on the day Avraham completed his 99th year He circumcised himself.” Nachmanides already queried this commentary, saying that seeing we accept the view of Rabbi Eliezer according to which the patriarchs were all born in the month of Tishrey, and this circumcision took place on Passover (the future date of Passover). In that case, Rash’is explanation would mean that the circumcision took place on what was going to be Passover. Therefore, Nachmanides understands the wordsבעצם היום הזה to mean that Avraham carried out the command on the same day it was issued. All male members of Avraham’s household were circumcised on that day, including his son Ishmael. The Torah tells us this in detail in order to compliment Avraham on the prompt execution of G’d’s command. Avraham circumcised himself last, as otherwise he would not have had the strength to circumcise his entire household which numbered probably more than a hundred, a considerable portion of whom were grown men. According to tradition Avraham observed all the commandments of the Torah, having divined G’d’s intent through his intellect. The question therefore is why he did not observe the rite of circumcision already many years ago, seeing that he knew that this would please the Lord? Some sages answer that this tradition that attributes to Avraham the knowledge of all the commandments which would be featured in the Torah, came to him only after he had circumcised himself. He advanced spiritually by giant steps as a result of having circumcised himself. This answer does not appear as likely, as if Avraham was intellectually mature enough at the age of three to recognize that there was a Creator who had created the entire universe, surely he had developed further intellectually in the 96 years intervening between then and the time when he circumcised himself. The more likely reason is that he wanted to wait until he was commanded to do so, as we have a rule that if one performs a commandment because it had been commanded by G’d, this is morally/ethically a higher ranking deed than doing the same thing without having been commanded. In the case of all other commandments Avraham knew that he would be able to perform the same commandment also after he would be commanded to do so. Removal of one’s foreskin is something irreversible, and will not be possible to be repeated again. Hence in this case Avraham waited until G’d issued His command.

That Avraham turned ninety-nine. You might ask: In v. 23 it is already written, “On that very day,” on which Rashi commented, “On the same day that he was commanded.” And in the next verse it is written, “Avraham was 99 years old.” [Why then is his age repeated here?] The answer is: Otherwise we might have thought that Avraham was over 98 but not yet 99, although it is written “Avraham was 99 years old,” because part of a year is considered as a whole year. Thus it is repeated “On that very day” to teach that [they were circumcised] on the day Avraham turned 99, and Yishmael turned 13.

בעצם היום הזה, “on this very day;” According to Rabbi Gamliel, Avraham sent a messenger to Shem, son of Noach, and invited him to circumcise him and his son Ishmael. Not only that, but the date was the tenth of Tishrey, i.e. Yom Kippur which during that year occurred on a Sabbath. He derived this from the use of the expression בעצם היום in Leviticus 23,29. [Presumably Avraham knew that performance of this commandment on the eighth day of a newborn child overrides the prohibitions of the Sabbath and even Yom Kippur. Ed.] This is why every year on the recurrence of that date, G–d reminds Himself of Avraham’s having performed this commandment and it is a factor contributing to atoning for all of our sins on that Day. In B’reshit Rabbah, there is a version describing that after Avraham had already had the knife and his foreskin in his hand to perform the circumcision on himself, he became afraid that he might tremble due to his advanced age. G–d thereupon assisted him and guided his hand; this is why we say in our daily prayers in the morning when relating to this event: וכרות עמו הברית, “He cut the covenant with him (Avraham).” The quotation is based on Nechemyah 9,8. The usual translation of the word, inaccurate is: ”He concluded” Ed.]

בעצם היום הזה, on the very same daywhen G-d had issued the command;

נמול אברהם, the day which later on would correspond in our calendar to the Day of Atonement was the day when Avraham performed the circumcision on himself. (Compare Pirke de Rabbi Eliezer chapter 29). If Avraham had divinedthe laws of the Torah through use of his intelligence, why had he not performed such an important commandment much earlier? It may have been in order not to discourage potential proselytes in the future. If people contemplating conversion to Judaism would have thought that the very first step in such a conversion was to be the painful rite of circumcision, they might have developed second thoughts. As to the question of why G-d had delayed the commandment until after He had concluded the covenant between the pieces with him, the reason was so that when he would sire Yitzchok, this son would have been the son of a fully fledged Jew already before developing in Sarah’s womb.