Because of what God's nature is for the satisfaction of justice. By American law, a person is punished for their own crimes, and God is mostly like that, but there is an exception. Someone else can pay for a person's sins if they meet certain qualifications. If they do, they are called a kinsman-redeemer. The Law given to Moses (a reflection of God's nature) about this is in Leviticus 25 (and snippets in other places). The book of Ruth gives us an illustration of what a kinsman-redeemer is. (Ruth 4)
To qualify as a kinsman-redeemer a person must:
1. be a blood relative. (Lev. 25:25, 49; Jer. 32:7-8; Heb. 2:11-14,17) [which is why God had to became fully man]
2. be willing to pay (Ruth 4:6, John 3:16, et. al.)
3. be able to pay (a slave doesn't have the authority to redeem another slave) [Jesus was qualified because he was without sin, Heb 4:15, Rom. 3:23; specifically, he was not a son of Adam, See Rom. 5]
Since the punishment for sin is death (Rom. 6:23), Jesus chose to die in our place.
Note that the above verses also reveal that Jesus redeemed mankind’s “land” (the Earth that God gave them but they lost when they became slaves to sin).
Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. (Mat. 5:17, 1984 NIV)
(Edited to add a verse reference [Heb. 2:17].)