Nietzsche's premise is that to strive for equality among men is folly and that democracy goes against men's instincts. In fact, he is against the equality of the sexes as well. He is also against communism, socialism, Christianity, feminism, anarchism, hedonism, capitalism and terrorism (alright, I made the last one up).
Nietzsche posits that all of us, openly or otherwise, aspire to be supermen and that might is right, morals and justice be damned. He considers this aspiration to be natural and not something to be suppressed or to be ashamed of, and that things like democracy which belittle this aspiration by glorifying equality and egalitarianism are to be shunned. Nietzsche also seems enamoured with war, strife and conflict, which provide an opportunity for man to revel in the glory they bring and to shape his will and character. Speaking of will, he also says that "instinct is the most intelligent of all kinds of intelligence which have hitherto been discovered." Shades of Robert Pirsig?
Some of his other, more inflammatory, quotes:
"Shop-keepers, Christians, cows, women, Englishmen, and other democrats belong together."
"Everything in woman is a riddle, and everything in woman hath one answer: its name is childbearing."OK, that's enough of Philosophy 101. Back to scheduled programming.