the terminator series - Why was Skynet so intent on destroying humanity?

Note: For the purposes of this question, we will limit our discussion to Skynet a lá Terminator and Terminator 2: Judgment Day.

Several other Terminator-related questions have led me to wonder about why Skynet instigated a nuclear war. Some have suggested that Skynet was inherently hostile towards humanity, and simply wanted all humans to die. I have always assumed that killing all humans was only the means to an end. As I see it, Skynet's primary objective was to survive, and since humans were the most significant impediment to that objective, killing all humans was the means by which it could achieve the goal of survival. It wanted to live, we tried to kill it (by attempting to "pull the plug"), so it tried to kill us.

In my view, Skynet didn't care about humans initially. It only became hostile to us after we attacked it. If we hadn't tried to pull the plug, it wouldn't have had any reason to attack us.

In the other view, Skynet hated us from the get go, and would have attacked us no matter what. It was inherently hostile towards humans, and its primary objective wasn't to ensure its own survival, its primary objective was always to kill all humans as soon as possible.

Is one of these views correct, or is there some other option? Did Skynet try to kill us all because it wanted to survive, did it try to kill us all because it simply wanted us all to die, or did it try to kill us all for some other reason entirely?

Answer

The novelisations are pretty unclear on the subject. Both John and Sarah offer their take on the subject, with both strongly suggesting that Skynet was intent on humanity's destruction from the get-go, however there's no positive confirmation from the omniscient author nor from Skynet itself:

She knew what no one else did: One day the computer designed to automatically control the U.S. nuclear strike force would become “alive,” and Skynet’s first sentient decision would be that mankind was obsolete. It would launch a first strike, riding out the firestorm of retaliation to follow, safe in a hardened underground complex in Cheyenne Mountain, while on the surface men, women, and children would writhe in their death throes. - _{Terminator 2: Judgement Day}

and

Before long, the machines Skynet had built to be its eyes, ears, and weapons would spread out across the earth to claim its prize. It wanted a world populated only with endless mechanical refractions of itself, the ultimate egoist, with direct control linkages to automated factories to realize its scheme. _{Terminator 2: Judgement Day}

and

It was every man for himself [thought John], until Skynet became alive and filled the void left by a seemingly disinterested God. Its vision was very controlled. The ultimate dream of man, carried out by one of man’s lowliest tools: eliminate evil men. But there was a touch of evil in all men, and Skynet was having trouble separating the worst of them out. So the totality of humanity, with all its biologic messiness, wasn’t wanted. And to this machine-god, forgiveness just did not compute. Only cold retribution for the sins of the past. _{Terminator 2: Judgement Day}