I'm a nihilist and I don't think that's true whatsoever. At least to be a moral nihilist, it just means I don't believe in any metaethical framework (no "oughts")
Regardless of whether or not I think killing me would have or create some objectively bad property, I have an egotistical attachment to living, and of course I'm going to try to avoid it.
My ethics and my desires are related but different.