I've had the same sort of discussion about Terminator 2.
When they blow up Cyberdyne Systems, everything should change instantly. Arnie wouldn't have been built, so they wouldn't have gone there to blow it up. But then, with no one to stop Cyberdyne Arnie would get built, then he'd get sent back in time...
It's a paradox, a loop in time, they can only exist together, you can't have one without the other, you cannot change the future.
For example,
I go back in time
I kill my Grandad when he's young
I'm never born and don't exist in the future
So I can't go back in time to kill my Grandad
He isn't killed, so I am born...