There are two basic approaches, to the dilemma of changing the past via time-travel:
1. "It happens, because it happened." (That's a famous sentence from a Sci-Fi-series.) Whatever you do, you can't change past. In the end, your actions will always lead to the future as you know it. Even your means of sabotage will accidentally lead to the future you tried to prevent.
2. The other theory is, that there are multiple manifolds/parallel universes, like a river spreading out into more and more channels. Each channel is a possible composition of events and attributes. But only one of these channels is reality.
You travel back in time and your action causes a universe that was virtual to become real and the future that was destined to become reality turns into a virtual future (a dead-end so to speak).
The problem with his argument is: What exactly has he done, how has he changed the present so the future as he knows it, won't come true?
Has he fathered a child? (And is its name John Connor?)
Did he save someone who was supposed to die?
Did he kill someone?
Has he delivered an outstanding idea or technology that changed the course of society as a whole?
Did he change the lives of one important or many ordinary persons?
The answer is No.
His actions were mere background-noise in the big scheme of things.
Accordingly, we now live in a present that was always supposed to be.
Accordingly, he's a quack.
There is one counter-argument to my reasoning, but that can be discarded:
Did his mere presence induce probability-fluctuations on classical and/or quantum-levels (the butterfly that causes a storm) that build up from a fractal level into changes of a magnitude that affect the history of a sizable part of earth?
Extremely unlikely, because blowing some air, flushing some water or kicking a can that flies into a car and causes a scratch only has an event-horizon of a finite size (order of magnitude: miles) far smaller than the system it is supposed to influence (order of magnitude: thousands of miles). This random influence is again droned out by the random noise of the millions and billions of people and trillions of random events around him.