The answer to OP is simple.
Look at little kids.
Some of them "go out" with each other, even if they're 5 years old. The two don't need each other for sex, protection or money... so why do they do it?
I know this will sound a little cheesy, but they do it for a little something called love. It's harder to apply this term in the teen or adult world, since guys and girls end up needing each other for sex, self-confidence or even money. However, there are a few people who do it simply because of love.