I have an idea.
The "original" John Connor was the lead computer programmer in a military defense system AI project, Skynet. Specifically, John was responsible for writing the parts of Skynet that were responsible for how it decided on tactics, maneuvers and (because he was the one that programmed it) intimately knew all of Skynet's strengths and weaknesses.
When Skynet launched Judgment Day, John was the best person to lead the "resistance" and fight against Skynet, specifically because he knew how Skynet would think and operate.
That's why Skynet decided he was the most important person to terminate to ensure it's own survival, even if Skynet didn't know why
John was the leader of the resistance.
Of course naturally Skynet wouldn't be aware that the lead programmer of it's tactical systems was a programmer nammed John Connor, after all, why would it know? It's not as if it would have a "credits" list in it's AI.