Take this statement by Ayn Rand as paradigmatic of strong ethical egoism:
“the actor must always be the beneficiary of his action and that man must act for his own rational self-interest.” SOURCE
How does ethical egoism account for concern for future generations, then? For long-term concern for the environment?
How does securing the happiness and survival for our posterity make us the beneficiary of this action?
Given that earth will only be around for a blink of the eye, and given that we couldn't destroy the earth due to our environmental bad habits in our life time, why not rape Mommy Nature for all she's worth? Slash and burn, baby.
To reply, "Because it makes me feel good about myself to work for a habitable and safe planet for people generations removed from myself," requires us to ask, "Why?" Why does it make you feel good to do something that allows others to be the beneficiary of your actions? That seems immoral on egoism’s terms. "Because it makes me happy." "Because it allows me to sleep at night." Why?
Ethical egoism seems to imply that we have no obligation to our posterity and our long-term environment. This seems false. Ethical egoism seems false, then.