Explain how the principle of equal treatment undermines ethical egoism as an acceptable moral theory?

Answer 1

The principle of equal treatment is the idea that a moral theory should treat all people equally, unless there is a morally relevant reason not to. In other words all people should follow a certain moral code unless there is a morally relevant reason that they should be exempt.

Ethical egoism is the idea that you should always act in accordance to what is in your own self interest. In other words an ethical egoist holds themselves in their own highest regards - in a sense discriminating against all persons but themselves. This is for no other reason aside "I am myself, and therefore look out for myself only". Depending on your point of view, the mere idea of "I am me" may not be considered a morally relevant reason to treat yourself differently.