"This is what happens when you find a man in the Alps!!!!"

What the heck is that supposed to mean?
Richard,
Among time travel movies, there is the closed loop kind (12 Monkeys, T2) and the rewriting/parallel universe kind (BTTF).
In the closed loop kind, what has happened has always happened. However, everything seems to have a genesis. I don't think you could be your own father in a closed loop movie. However, you could send your friend to be your father. Your father appears in the past because you will eventually send him. And the person your choose in the future you already know will become your father. Even if you tried to send someone other than Kyle Reese, Kyle Reese will be the one that goes, no matter what. Nothing ever changes.
In the rewriting type, new braches are created when you go back and change things. You could have Kyle Reese be your father, then go back and change it into someone else by delaying him, and may even negate your own existence. They waver on if your original timeline stuff remains even if you invalidate it or treat it like BTTF where errors are erased from existence.
For the Terminator series, three things always happened. There was always a judgement day. Miles Dyson always was inspired to create the Terminator, and the original Cyberdyne lab and the original Terminator artifacts were always destroyed. The devices created in T3 were based on the work that Dyson had already completed, so the artifacts were no longer needed. For that reason, the T-800 exists unchanged and the T-1000 also exists unchanged.
The only flawed thing in the Terminator series is Skynet's belief it could change the past. However, it always had to try because it could not exist if it hadn't tried to kill John Conner by sending a T-800 back in the past.
T3 busted up all kinds of continuity, as do the deleted scenes for T2. But overall, T2 should still work if Sarah is indeed wrong that the road was completely open at the end of T2. She only thought she had change things when instead she was doing everything she would ever do and the end result depended on her attempts to stop it.
Thought of another portion of some favorite films that bug me:
I love the remake of
The Ring. Everything in it really worked for me tonally except the opening. The girl at the end of her seven day cycle was not acting as she should, and should not have been told the urban legend by her friend. Changing this opening to make the soon-to-be victim morose and having her friend find the body would have worked much better than the pillow fight Scream antics they used.