וַיִּקְרַ֥ב אַהֲרֹ֖ן אֶל־הַמִּזְבֵּ֑חַ וַיִּשְׁחַ֛ט אֶת־עֵ֥גֶל הַחַטָּ֖את אֲשֶׁר־לֽוֹ׃
I przystąpił Ahron do ofiarnicy, i zarznął cielca zagrzesznego za siebie;
Or HaChaim
ויקרב אהרון אל המזבח, Aaron approached the altar, etc. This verse alludes to a conversation in the celestial spheres which is reported in the Jerusalem Talmud Makkot 2,6: "They enquired from 'prophecy': what shall be the punishment of a person who has sinned? Answer: והנפש החוטאת היא תמות. 'The person (soul) who sins, she (the soul) will die (Ezekiel 18,4)'. When they asked 'mercy' the same question the answer given by 'mercy' was: 'he shall bring a sacrifice.'" The major factor determining the value of the animal sacrifice is the thoughts it evokes in the person offering it. If that person will realise that everything which is being done to the sacrificial animal is something that should really be done to him, the offering may effect atonement for its owner. When the Torah writes that Aaron approached the altar this is another way of saying that he readied himself to place his own soul on the altar as a guilt-offering. He was aware that when he performed the act of slaughtering the animal instead, this was an act of mercy by G'd who spared his life and allowed him to present the animal's life as a substitute for his own.
Tur HaArokh
ויקרב אהרן אל המזבח וישחט, “Aaron approached the altar and slaughtered;” Nachmanides writes that in his personal view, the plain meaning of the words קרב אל המזבח is that Aaron is to approach the north side of the altar where he is to perform the procedures involving the sin offering and the burnt offering, seeing these two types of offerings need to be slaughtered on the north side of the altar. (Zevachim chapter 5) The catching of the blood of these offerings must also be carried out on the north side of the altar in the appropriate vessels. Moses recorded this in abbreviated form as Aaron was already familiar with the procedure. According to a Midrash, seeing that Aaron was a קדוש ה', someone sanctified by Hashem, his life having been stained only by one marginal sin, his involvement in the sin of the golden calf, this sin was something which preyed on his mind constantly, similar to David’s remark וחטאתי נגדי תמיד, “and I am constantly conscious of my sin against You.“ (Psalms 51, 5) He felt that the image of the golden calf constantly intruded upon his imagination and interfered with the proper concentration required when presenting sacrifices on behalf of others. This is why Moses tried to restore his mental equilibrium by telling him not to be depressed, that G’d had already forgiven his involvement in that sin. Some commentators think that it had been Satan that had shown Aaron these images of the golden calf, and that Moses told Aaron that in spite of he fact that as far as G’d was concerned, his sin had been forgiven, he also had to do something to shut up Satan so that the latter would not be able to upset him at the crucial time when he would perform sacrificial duties. This is the approach taken to our verse by Torat Kohanim.
Ibn Ezra
his It was from his own property, as is the bull of Yom Kippur [16:6].