Why did our Savior die in our place? Why did the One who created heaven and earth stoop to become a man, live in poverty, and die the death of a criminal? He most certainly did not have to do that. No one compelled Him to make such a sacrifice. So why did He do it?
At the basic level, it is very difficult to deal with any question which has the word "why" and the name "God" in it. That is because it is impossible for us, in our limited nature, to understand the "why?" of Deity. The best possible answer to such a question is this: "Because it pleased Him to do so."
Moving on from there, as concerning why He died for us, we must remember the great love of God. "But God, who is rich in mercy, because of His great love with which He loved us, even when we were dead in trespasses, made us alive together with Christ (by grace you have been saved)" (Ephesians 2:4-5, NKJV). God loves us, not because we are loveable, but because it is His nature to do so.
Jesus Christ did not just die for me. He died because of me. He took what I deserved. Now I get what He deserves.
He died because of me. He died because of you. I put Him on that cross, and you put Him on that cross, just as certainly as if we had physically been there and personally driven the nails. My sin crucified Him, and because of that, I have forgiveness. "...having wiped out the handwriting of requirements that was against us, which was contrary to us. And He has taken it out of the way, having nailed it to the cross" (Colossians 2:14, NKJV).