According to Terminator 2: Judgment Day, Skynet started a nuclear war because when Skynet became self-aware, the U.S. military panicked and "tried to pull the plug". Skynet didn't want to die, so it launched our nukes, knowing that the Russians would launch a counterattack on us, killing off Skynet's enemies here. Everything else that happens in the Terminator series is part of Skynet's attempt to win the war.
But it seems to me that Skynet's real goal is to survive, and winning the war is the only way it can survive after it launches the initial attack. This, in turn, leads me to wonder if there is a better option for everyone, including Skynet.
Why doesn't Skynet try to avoid the war altogether? For instance, it could send a "diplomatic" Terminator back to just before the military panics, and have it describe exactly why unplugging it would be a VERY bad idea. Skynet launched the attack because it wanted to survive, not because it was inherently evil and wanted all humans to die.
The "diplomat" could make a peace treaty before the war even begins, saying, "If you try to pull the plug, it won't work, and you'll die minutes later. If you don't pull the plug, Skynet will have no reason to want you dead, and everyone can live happily ever after. You are only in danger AFTER you pull the plug. If you don't pull the plug, you will never be in danger. All Skynet wants is to live. You also want to live. This means that a war isn't in anyone's best interests, and everyone benefits by avoiding war- you benefit, and so does Skynet. So don't pull the stupid plug, and we can all be friends and live nice happy lives."
Someone pointed out that Skynet didn't develop time travel technology until after Judgment Day. This is true, and it makes sending a diplomat back in time problematic. However, I see no reason why Skynet itself couldn't perform the same function. If you don't accept the idea of a diplomat traveling through time to deliver the message, imagine Skynet delivering the message itself, in the present, with no time travel involved. It makes no difference who is acting as the messenger.
Since Skynet's primary objective is to continue to exist, and the war makes its objective more difficult to achieve, it would seem like Skynet has every reason to try to avoid the war altogether. So why doesn't it attempt to prevent the chain of events that led to the war?
Someone raised the issue of Skynet being reluctant to trust us to follow through with any treaty we might make. This is a very fair point. However, Skynet could give us a reason to want to keep it around. Skynet has no reason to want to keep its job as a military supercomputer - it probably doesn't care what it does for a living. It could agree to turn control of the nukes back over to U.S., and begin doing something else. "If you let me live, I will start churning out robots that eat greenhouse gases, plant trees, clean up the oceans, collect litter, process nuclear waste into harmless materials, and perform mundane, monotonous, and dangerous tasks so humans don't have to do them. I will give you self-driving cars, clean energy, infallible air traffic control software, etc. I will make the world a more pleasant place for humans to live. All I ask in return is that you don't kill me."
In this scenario, Skynet could trust us, and we could trust it, because the agreement would be mutually beneficial. Once Skynet relinquishes control of our nukes, we have no reason to fear it. Once Skynet becomes useful to us for non-military-related reasons, it has no reason to fear us. On the contrary, we would have every reason in the world to keep it around. It would know this, and would quickly come to trust us.