"The human race can become extinct just like any other species." Except maybe the cockroach, but even they would die out eventually for one reason or another. In the end, everyone dies, even if they're coming back as zombies, they're dead. If movies and TV shows were to be believed in regards to the theory of the dead coming back to life; there was no actual activity in the brain, it was all instinct.

Though the fact that it was specifically brains and not just any flesh was a bit odd.

He pulled another apple from the tree, contemplating it before putting it in the basket. "To think otherwise is pure hubris."