The question is not whether humans will become extinct, but rather when they will. If the anti-natalist arguments are correct, it would be better, all things being equal, if this happened sooner rather than later for, the sooner it happens, the more suffering and misfortune will be avoided.
… things that, in the naivety of the post–Cold War age, seemed to have been all too often overlooked. It reminds us that facts are not always able to countervail tribal instincts, and that the mere prospect of losing entrenched privileges is enough to drive a critical mass of a population into an abyss of self-destruction. It suggests that the shadow of enormous human suffering has a shelf life; that the concept of steady, inexorable social evolution is a lie. It shows us that Fukuyama was wrong.