At first i had some trouble differentiating this from psychological egoism. They're based around selfishness, but the difference is between selfishness opposed to self interest. Psychological egoism states people should always pursue their own interest, but ethical egoism is a normative theory that explains how we ought to behave in our best interests. psychological egoism supports immediate pleasures such as excessive drinking and smoking, and ethical egoism frowns upon things like that.
Ethical egoists are not opposed to doing things for others as long as it crosses over into their best interests as well, but it has to benefit them directly. They also do not believe in charity because they see it as rude and intrusive.
I definitely don't agree with this, but I've met people who always have a self motive in everything they do. Society wouldn't work properly if everyone thought this way. We rely so much on each other, and if everyone only thought of themselves, people would rarely do anything to help others in need, and we all go through times of need. This kinda comes out of left field, but I also think compassion is ingrained in the human race as a survival method because we cannot survive successfully without companionship and compassion from others.