If you're truly selfish, you will never act selflessly - it will only be a pretense. If you're truly selfless, then selfishly accruing resources will actually help other people, as you're likely to use them on your not-self.
(This is an expanded version of something Jehu helped me find the words for.)
I take as proven that in any conflict, the less selfish should win, as it causes less collateral damage. If satisfying values is good for one person, then it must be better for more people. Only, the truly selfish will never bow to this principle - by definition, they do not care about anything I might care to use in my argument. Ergo, if in trying to be selfless you let someone else go first, most likely you just harmed more people than you helped.
This can all be derived from psychological egoism, though I do admit the use of 'selfish' in this context can be misleading.
Psychological egoism is true simply because actions follow from goals. You can try to act according to Chappell's definition of selflessness, but that means setting the goal of contradicting your own goals. If you succeed, all it means is that you valued the selflessness goal over other more 'selfish' goals, which means you're still maximizing your own selfish values. (And if you fail it means you succeeded at your other goals.)
What does this imply? This implies that there are those selfless in Chappell's definition. They're the ones that value the values of others as well as their own purely personal values.
When such a person acts selfishly, maximizing e.g. their own warm fuzzies, they help others.
Which in turn means selfishness, in its true philosophical definition, is nothing to be ashamed of. And, as I hope I've shown, anyone who is truly selfish in Chappell's narrow sense will never admit it, as long as selfishness is considered bad.
It is not only pointless to consider selfishness bad, but counter-productive. It it simply a barrier to combating narrow selfishness.
This is not a coincidence. If you were narrowly selfish and wanted to get your natural opponents out of the way, is this not exactly how you'd try to twist them into knots? Certainly, if I ever decide to embrace solipsism, it is exactly what I'm going to do.
Now I'm going to do the same thing from the dark angle.
Assume it is good to be selfish. This proves it isn't good to be selfish - it's a wrong question, not even wrong situation.
If it is good for my opponent to be selfish, it must be good for me to be selfish, by symmetry. It is selfishness that is good, not the particular person being selfish. And I happen to think it would be better if I won. Therefore, their belief in selfishness means that my beliefs imply I should win.
Verification: what if it isn't selfishness per se that's good, but the person? Then I've again proven that selflessness is better. If one person is good, then I just find two people that add up to being more good.
No matter what argument you start with, it proves that every individual should fight unreservedly for the selfish values. If there were an argument that was only an impediment to the narrowly selfish, I would advocate that. But, as above, there cannot be.