Why did John Connor want to stop the killing of Miles Dyson?

Question

Aside from being against the killing of others, why did John want to stop Sarah from killing Miles?

The T-800 said that Dyson's death could possibly prevent future events from happening, but John pressed on and Miles was spared.

Is there another reason John had for stopping Sarah?

Answer 1

Is there another reason John had for stopping Sarah?

TL;DR

No.

Explanation

Does he need another reason? As John says to the T-800:

I don't care!! There's gotta be another way. Haven't you learned anything?! Haven't you figured out why you can't kill people?

Look, maybe you don't care if you live or die. But everybody's not like that! Okay?! We have feelings. We hurt. We're afraid. You gotta learn this stuff, man, I'm not kidding. It's important.

This is the key theme of Terminator 2: It's not okay to go around killing people just because it's convenient.⁽¹⁾ This belief is what separates the heroes from Skynet. The theme manifests in a number of ways throughout the film.

The scene immediately before John and the T-800 arrive at Dyson's house is a turning point for Sarah Connor. She was traumatised by the events of the first film. She fears and hates the Terminator above all else, but has also chosen to become the Terminator. Like the Terminator in the first film, she tries to kill her enemy's "parent" so that her enemy can never exist.

When Sarah reaches Dyson's house and

chooses to lower her gun, even though Dyson is injured and helpless on the floor in front of her

this is a crucially important decision for her character. At the last moment, she rediscovers her humanity and her capacity for mercy.

Before John decided to go after Sarah, the plan was for him and the T-800 to leave Enrique's compound and cross the border into Mexico. It would be logical for John to lie low, hide from the T-1000, and wait for Judgment Day so he can fulfil his destiny as leader of the resistance and eventually destroy Skynet.

However, John refuses to go down this path. Instead, at great personal risk, he goes to stop Sarah and then

destroy the Cyberdyne facility.

John does this because he believes trying to save three billion lives is better than allowing the war to happen, even if the latter course will result in his victory over Skynet.

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⁽¹⁾ It says something about the moral universe of Hollywood action films that it seems weird, even incomprehensible, for a protagonist to believe such a thing.

Answer 2

• The novelty of a human teaching a cyborg humanity (although he was directly stopping Sarah Connor, the T-800 was standing by, and John had been spending the movie trying to teach the T-800 that you can't just go around killing people). The writers also needed John's character to stop Sarah so that it would be congruent with John stopping the T-800 from killing people earlier in the movie. Note also that only shortly thereafter, during the facility break-in, the T-800 emphasized a no-fatality approach to subduing all security and police. The theme of a human teaching a machine humanity is omni-present in Star Trek: The Next Generation. It has merit as an artistic endeavor; as an analysis of human nature, morality, and as a Sci-Fi trope.
• John Connor has a conscience. It's probably hard in 2017 to comprehend that not every 15-year-old in 1991 was a cold-blooded killer. There has been a movement in America to erode compassion for many years, which might color your perspective; but back in 1991, compassion and morality were completely the norm. It wasn't some major brainteaser like "The protagonist doesn't condone murder?? Why???" It's common for a protagonist to have a moral code, and asking why a protagonist doesn't condone murder (although I respect your right to ask the question) is like asking why the hero of the story doesn't kick a handicapped senior citizen.
• It's a common theme in art that if you win the war while abandoning your own principles, then you have really lost. This is another theme that shows-up oddly frequently in Star Trek: The Next Generation.
• Although it may not have been immediately apparent to John in a split second, killing Dyson would not have actually won the war against Skynet. Recall that only two minutes later in the movie, Dyson explained that even if he quit his job, other researchers could still follow his work, therefore it must all be destroyed. Yet, despite destroying all of Dyson's work, we still got a Terminator 3, Terminator 4, etc. In other words, if you've oversimplified the situation into thinking that killing Dyson would end Skynet, then you're wrong, because it wouldn't have, it didn't; and furthermore, even more thorough measures like destroying Dyson's research (on top of Dyson dying at the facility and liquefying both terminators) were still not enough. By not killing Dyson, the Connors gained an ally who could significantly assist in destroying the work; which is itself a moral lesson in cooperation.