You can reduce every possible motivation to selfishness if you like, but that makes the term kind of useless; if all choices are selfish, describing a particular choice as selfish has zero information content.

Accordingly, trying to maximize happiness for everybody can be seen as purely selfish. Either as an effort to survive, by making everybody wanting to make everybody else happy, given that not you but somebody else wins. Or simply because it makes oneself happy.

You should be more cautious about telling other people what their motivations are. I would die to save the world, and I don't seem to be alone in this preference. And this neither helps me survive nor makes me momentarily happy enough to offset the whole dying thing.