Because man had sinned against God and thus owed God the payment for sin which is death, only a human’s death could atone for sin. However, only God could achieve our salvation. Because our sins are against an infinitely holy God, they are infinitely heinous and worthy of infinite punishment. The only way a finite human being can pay for his/her sins is by spending infinity (eternity) in hell. Because Christ is infinite God, He was able to bear the infinite (eternal) punishment for all the ones given to Him by the Father in a finite amount of time (as He hung on the cross). Only the God-man could achieve our salvation! As Anselm said in his theological masterpiece, Cur Deus Homo? (literally “Why God Man?” or “Why Did God Become Man?”):
It would not have been right for the restoration of human nature to be left undone, and . . . it could not have been done unless man paid what was owing to God for sin. But the debt was so great that, while man alone owed it, only God could pay it, so that the same person must be both man and God. Thus it was necessary for God to take manhood into the unity of his Person, so that he who in his own nature ought to pay and could not should be in a person who could . . . . The life of this man was so sublime, so precious, that it can suffice to pay what is owing for the sins of the whole world, and infinitely more.