"The first thing to understand is the role of the priesthood in the Old Testament. Whenever an Israelite sinned and had to make atonement they didn't make atonement themseves, but instead had to give their offering (e.g. sacrificial goat) to the priest, and "the priest would make atonement for them" (see Lev 4:20; 4:26; 4:31; 4:35; 5:6; 5:10; 5:13; 5:16; 5:18; 6:7). In other word, God uses holy mediators between Himself and sinners, in this case priests. Some might mistakenly think that the person's guilt was transferred to the sacrificial animal during this process, but that's simply not in the text, and it's erroneous because it would negate the whole purpose of the Priesthood. The lamb was not taking the punishment of the individual because it was only after the Priest had gone through the rituals of the sacrifice after the animal was dead that atonement was made. See Leviticus 4:22-35, where the duties of the sinner (bringing and killing the animal) and the duties of the priest (making atonement) are distinct."
"These texts [Exodus 28:36; Leviticus 10:17; Numbers 18:1] are fascinating because it directly links the priest's act of "making atonement for them" with that of "bearing their iniquity." In other words, when a priest is said to "bear iniquity" of a sinner, it means the priest takes on the responsibility to "make atonement" for the sinner. It does not mean the guilt is imputed to the priest so that now the priest himself becomes guilty."
"Once one realizes the role of the priest in "bearing the iniquity of the people," carrying this over to the New Testament we see Jesus' role as High Priest in a more mature light. Clearly, when texts like Isaiah 53:11 and 1 Peter 2:24 speak of Jesus "bearing our iniquity," it refers to His role as High Priest taking on the burden of making atonement for other people. Thus, in "bearing sin" Jesus was not "guilty" in our place. This can be seen even in the contexts of Isaiah 53 and 1 Peter 2:24, which I'll briefly turn to.In Isaiah 53:6, it says "the Lord has laid on him the iniquity of us all." It turns out, this same Hebrew word for "laid" is used a few verses down, in verse 12, "he makes intercession for the transgressors." That same Hebrew word is translated to mean "make intercession," showing clearly that "make intercession," and "make atonement for" are synonymous with "bearing sin,"