So, a couple nights ago, I was thinking about Jesus being both God and Man, and what His sacrifice on the cross meant. It's a contradiction in terms, to be both fully God and fully Man. Man is a creation, not worthy to be worshiped. God is the creator, a being outside of space and time, and not only is worthy of honor, but requires it by His nature. Man is finite. God is infinite.
It's kind of like in Doctor Who, "The Big Bang" where the 11th Doctor "restarts" the universe. The Pandorica can fix the problem, but is finite, and an infinite amount has to be fixed. For some as yet unknown reason, the TARDIS is exploding and destroying infinitely. The solution is to combine the Pandorica's solution, to the TARDIS's infiniteness, so the universe is fixed at every point in space and time. Now, Doctor Who isn't really Catholic at all, and sometimes could be interpreted as rather misunderstanding Catholics, or at worst subtily anti-Catholic.
But it is an analogy. The first humans God made, Adam and Eve, disobeyed God and caused an infinite rift in relations between God and Man. It was Man's fault, and only a human can make retribution to God, but God is infinite, and so no human God made could possibly ever make retribution. Jesus is a divine person (not a human person, but fully human) and so Jesus could provide the ability to do things infinitely. He became fully human to make retribution, and could do so infinitely because He was God.
How did Jesus make reparation? Through Adam and Eve, everyone is born with original sin: a separation from God and a proclivity toward separation from God. Thus, even after baptism which removes original sin, the proclivity still exists, and causes everyone to fall at some point. Every action has its consequence, and the just consequence of sin is death. God is life, sin is turning away from God, and thus, is turning away from life. In the Old Testament, God gave the Israelites a finite reparation of their sins, which was the sacrifice of pure animals. Jesus sacrificed himself, taking upon himself all the infinite sins of everyone that would keep them from heaven if they wanted to go.
Why did Jesus die on the cross? Because we are all made in the image and likeness of God, and God doesn't make junk. He loves us more than anything else He created because He knows we can be like Him and He wants us to be like Him. We are imperfect now, but we can become perfect. God wants everyone to go to heaven!