Neitzche purposely attacks the notion that selfishness is unethical on two fronts:
1) It saves us from modernism and detachment -- In works like 'The Gay Science' and 'Thus Spoke Zarathustra' he diagnoses the loss of vigorous attachment to religion and philosophy in Europe after the advent of modern science as the effect of the accumulated weight of a morality that undercuts selfishness.
As modernism progresses, we are betraying the natural animal attachment to power and becoming abstractly alienated from reality. Real productive power seems to appear in our lives only to the degree we stop thinking so much about it.
The common interpretation is that we have overthought things and discovered that life is inescapably complex, and decisions need to be calculated with a cooler head. But that is just calumny against thinking.
Instead, this is because the intelligent have chosen the good of the whole over real investment in our own individual lives, and an abstract 'long-term quality of life' consistent with a 'rising tide that lifts all boats' over investment in enjoying the moment.
2) It corrects for the excesses of Christian humanism -- In 'The Genealogy of Morals' he points out that the motivation for the origin of a philosophy based upon the value of selflessness is itself an indirect form of selfish violence.
It is the psychological revenge of the previously losing class, who traditionally had little chance of gaining usable power. By allowing Christianity, based upon support of the poor and informed by monastic asceticism, to elevate poverty to a virtue, and also allowing the poor more voice in government, we have attacked natural selfishness too stridently. (We should only have done one or the other.)
So, in fact, the position is deeply hypocritical and wastes our effort supporting pointless lies and internal contradictions, instead of living.