Sinclair Ferguson on the atonement:

Atonement was impossible without an incarnation. Hebrews explains why the Son of God “had to be made like his brothers in every way.” It is so “that he might make atonement for the sins of the people” (Heb. 2:17, NIV).
   Our salvation requires not only the conquest of our enemy, Satan, but the removal of a yet more terrifying enmity: the wrath of the holy God of heaven. “Purification” and “atonement” must be made “for the sins of the people” (Heb. 1:3; 2:17, NIV).
   This was made clear to the people of God in the Old Testament by the constantly repeated ritual sacrifices they were required to make. They thus learned that they deserved death because of their sins; but they also were taught that in grace God Himself provided a sacrifice to take their place.
   However, even an Old Testament believer could see that the animal sacrifices couldnot in themselves make adequate atonement (Heb. 10:11). Otherwise there would have been no need for them to be repeated. The flesh and blood of bulls and goats could not atone for the sins of human flesh and blood (Heb. 10:4)! Only human flesh and blood could be an appropriate substitute-sacrifice. So the author of Hebrews says:

When [Christ] came into the world, He said:
“. . . a body you have prepared for me.
In burnt offerings and sacrifices for sin
You had no pleasure.
Then I said, ‘Behold, I have come—
In the volume of the book it is written—
To do your will, O God.’”

—Hebrews 10:5–7

   Jesus offered Himself as the substitutionary atonement!
   Sometimes theologians have spoken misleadingly, as though the incarnation is itself the atonement (the “at-one-ment” of God and man in Christ). It is not. But without it there could be no atonement. He took our nature in order to bear our punishment. Only thus can we be at peace with God.

—Sinclair Ferguson, In Christ Alone: Living the Gospel Centered Life (Reformation Trust, 2007), 26–27.