I guess it might depend on the apocalypse, but could you provide an example?

Sure. The most basic antinatalist argument is that creating a new human life on average creates more disutility (in the form of human suffering) than it creates utility (in the form of human happiness). Whether or not you accept this argument depends on what you think the prospects of suffering and happiness are for the average human life.

At present, I view human lives as involving potentially very high gains. Nuclear war would not only stop the potential for many such gains, but it would likely halt or reverse gains that have already been made. For instance, absence of access to modern medical techniques, dentistry, painkillers, etc. would likely create substantial suffering.

On the plus side, it would also make life shorter, but I have a feeling that would be cold comfort-- at least to non-antinatalists!

The View from Hell provides a solid overview of a lot of antinatalist thought if you're interested in learning more.