Do animal rights activists fight for animal rights because of psychological egoism?

Not at all. Actually animal rights activists fighting for animal rights show obvious signs of altruism, although they might be misunderstood or misquoted such as what happened around the nomination of famous animal rights activist Cass Sustein in the Obama administration. Animal rights activists include all sentient beings in their moral concern.

It is usually argued that those who don't understand rights cannot have rights. This is of course a major fallacy which would deny human infants rights just because they have no concept of rights.