system
Given the following post, respond as if you're commenting on Reddit:
human
My Philosophy Teacher told me that Nietzsche was a Nihilist, how?

How is that possible? is he wrong? 
Was Nietzsche a nihilist?
gpt
It matters what you mean by nihilism.

If nihilism is the denial of objective meaning and value, then Nietzche is absolutely a nihilist. When Nietzche denies being a nihilist, he means that rejection of objective meaning and value doesn’t cause him to despair. When he says Christians are the real nihilists, he means Christian morality is (in his view) life-denying.

But, clearly “nihilism” doesn’t mean the same thing in all three cases.