There's another side to anti-natalism, and that's the prevention of suffering. The argument goes that:

• we should all strive to prevent someone else suffering whenever possible
• all lives are going to involve a lot of suffering, from minor annoyances to utter tragedies
• therefore choosing to bring another person in to the world is choosing to increase the level of suffering

I can actually see that argument, and it's not narcissistic. But it also rests on the assumption that joy doesn't offset suffering, that they're essentially two different "accounts" and it doesn't matter how much joy you have in your life, the goal should always be to avoid suffering. That doesn't seem like an accurate assessment to me since basically all of human history shows that people will gladly accept a little suffering for more joy later.

So, I don't think all anti-natalists are anti-children (or anti person), they might be really trying to do the right thing, just based on different assumptions.