Who Did Jesus Die For?

No, I'm not thinking of the third point of Calvinism (if you're interested in thinking about the question that way, I'd recommend this sermon).

In 2 Corinthians 5, Paul writes:

"We have concluded this: that one has died for all, therefore all have died; and he died for all, that those who live might no longer live for themselves but for him who for their sake died and was raised."

So Paul says that Jesus died for us ("for their sake", v.14). It is good and right for a Christian to say and love the truth, "Jesus died for me." But in the same sentence he writes that Jesus died for us, so that we might live for Him.

So did Jesus die for us, or for Himself?