"Skynet never made any sense because it considered humans a threat, but there was absolutely nothing threatening about humans."

From the Skynet wiki

"When Skynet gained self-awareness, humans tried to deactivate it, prompting it to retaliate with a countervalue nuclear attack"

I would probably do the same thing, wake up and everyone around me is freaking out, trying to kill me, also I'm a newborn, also I have a nuclear button.

Isaac Asimov's I Robot does a fantastic job of showing how simple logical rules might not be ready for the complexities of everyday life