> A real nihilist in my opinion would probably kill themself

Nihlism is acknowledging that many if not all aspects that result in "life" are pointless. I fail to understand how that equates to no will to live life. There is only irrationality to living while acknowledging the pointlessness of it. According to the nihilist, every other justification is flimsy at best, so justifying the pointless is equally irrational to them.

Regardless, I think there are a lot of misjudgments about such philosophy, particularly with associating with some destructive impulse or depression etc.