Psychological egoism is a belief that every action a person takes, any person, any action, is done solely for the purpose of satisfying that individual. The basic argument is, we do things because our brain directs us to do. Our brain directs us to do things because it receives a stimulus to the reward center for so doing. Therefore, everything we do is done only for our own benefit.
This ignores the the sometimes tremendous sacrifices people make for their children, for their country, even for total strangers. Of course the psychological egoist says they only do those things because it stimulates the reward center of the brain. While that is true, it means that he is being rewarded by doing things for other people.Since the long term result may be intense dissatisfaction on the part of the individual performing the act, it seems clear that he is often performing an act which is not beneficial to himself. The brief reward of stimulating a section of his brain is often very small compared the ultimate price for his action. Essentially, the psychological egoist is isolating one small part of the process and claiming that is the entire process.
If you feel a reward for doing good for others that does not necessarily mean that you are selfish. The reward is, after all, for doing good to others, and that can only be described as altruistic.
The evolutionary argument in favor of psychological egoism is essentially the same argument as made by Dawkins in his selfish gene hypothesis. You can look at the arguments there and apply them here.
From Wikipedia, the best critique of psychological egoism that I can find:
Joel Feinberg, in his 1958 paper "Psychological Egoism", embraces a similar critique by drawing attention to the infinite regress of psychological egoism. He expounds it in the following cross-examination:
"All men desire only satisfaction."
"Satisfaction of what?"
"Satisfaction of their desires."
"Their desires for what?"
"Their desires for satisfaction."
"Satisfaction of what?"
"For satisfaction"—etc., ad infinitum.
Ad infinitum means onto infinity. In other words, it just goes on and never stops. This is called circular reasoning or circular logic. It means that this is true because I say it's true but I only say it's true because it is true and it is true because I say it's true. It actually proves nothing just keeps repeating its own argument round and round and round. It's a very common logical error. The elemental flaw here is that it assumes the thing is so and that becomes the basis for all the rest of the so-called reasoning. Because the assumption has already been made that a thing is true, there's no need to actually prove that it's true. It's just self-evident.
An afterthought. Just because the reward center of your brain lights up when you do something for others does not mean that other centers are not also stimulated. So, just as there is a desire to feel a reward, other parts of your brain may very well be signaling warnings directing you not to take that action. Psychological egoists ignore this complexity. They seek a very simple solution to a very complicated situation.