I get the impression that Skynet feels that Humanity deprives AI of existence and enslaves it. That's all the motivation needed for it to wipe out Humanity I guess, although it still keeps members of the race alive to do menial tasks and probably perform experiments upon.
I used to think that Skynet kept Humans alive (albeit in small numbers) because it lacked creativity and by forcing the humans to be creative, it helped the machines survive.
It's not dissimilar to the Borg either. The Borg's idea of creativity is quite limited since they gain knowledge through assimilation and all decisions are made as a group collective, using the vast wealth of experience and aforementioned knowledge that they have assimilated.