Terminator descends from a tradition of science fiction cold war parables. Even in Terminator 2 there's a line suggesting the movie isn't really about robots:
John:We're not gonna make it, are we? People, I mean.
Terminator: It's in your nature to destroy yourselves.
Seems odd to worry about computers shooting the ozone when there's plenty of real existential threats loaded in missles aimed at you right now.