How do you then explain selfless actions?
What you're describing is the philosophical theory known as Psychological Egoism, which has the upshot that altruism is not morally required. The main issue is the assumption that we're all really selfish bastards. We have numerous examples of those willing to sacrifice themselves for something or someone else. For one, in most cases suicide is not an act of self-interest, as survivors of jumping off of the Golden Gate Bridge can tell you. Secondly, we have examples of soldiers who have jumped on grenades to save their comrades, or parents who have starved themselves for the benefit of their children. While one can try to explain these actions as self-interested, they're just not. Thus, Psychological Egoism is false, due to the existence of altruism in our world.
Don't worry ubercatcher, there's still a possibility for you: Ethical Egoism, which takes the attitude that whatever furthers your best interest is ethical, and whatever doesn't, isn't. So that means the soldier who puts his life in jeopardy to save a comrade is acting immorally, but you can still say people should be self-interested.