"altruist (plural altruists)

1. One imbued with altruism; one who wishes well for others, not themselves."

So tell me how this conflicts with an egoist?

1. a self-centered or selfish person (opposed to altruist).
2. an arrogantly conceited person; egotist.
3. an adherent of the metaphysical principle of the ego, or self; solipsist.

If I am an egoist and I only think about myself and an altruist also think about others, I'll do things for myself and the altruist will do things for himself and for others, so there is actually no conflict unless the egoist harms other people, which is not included in the definition