The New Testament tells us that Jesus was fully man as well as fully God. This “incarnation” of God is a mystery, but is clearly taught throughout Scripture. As Paul tells us in Philippians 2:5-9, Jesus had “stripped himself of all privilege by…being born as a mortal man.” God didn’t die on the cross, since that is impossible. It was Jesus the mortal man who suffered and died on the cross for our sins.
That leads to the question of: Why it was necessary for Jesus to die? Since God is all powerful, why couldn’t he have forgiven sins in some other way? In a sense, that is like asking a court judge why he doesn’t simply let a rapist or murderer go free. God’s perfect justice requires that sin be punished.
The Old Testament sacrificial system required a sin offering “without spot or blemish.” The spotless lamb was then sacrificed by having its blood shed on the altar. However, the lamb was only a foreshadowing of God’s perfect Lamb who would one day be offered “once and for all” to pay our sin debt in full.
Although God didn’t die on the cross, it was necessary for this perfect sin offering to be God, since only God could live a life of moral perfection as a man. Jesus is the only person who ever lived without sin. Therefore, as a sinless man, Jesus is the only one qualified to be our mediator to God. Paul writes to Timothy:
For there is one God, and one mediator also between God and men, the man Christ Jesus. 1 Timothy 2:5, NASB
For further reading, we recommend the Y-Jesus article Is Jesus Relevant Today?