The grandfather paradox is a paradox of time travel in which inconsistencies emerge through changing the past. The name comes from the paradox's common description: a person travels to the past and kills their own grandfather before the conception of their father or mother, which prevents the time traveller's existence.
Now you have to start somewhere and so why not start with talking about the main idea used as to why some folks say time travel doesn't or can't exist. Before we go to far into this, lets just say this is not singling out grandfathers. It can be any event or persons which the person going back in time interacts with.
The thought process is, that you would go back and kill (which seems a little extreme) But is mostly used for the like of Hitler. You go back kill Hitler, then WW2 and the Holocaust never happens, but the problem then says "Well if you have stopped the Nazis from rising then you wouldn't have a reason to create time travel and you wouldn't go back in time to kill Hitler"
Similarly with all other events, your action to go back would effect the future to a point that you wouldn't have invented time travel, or have a reason to go back in time. But surely that only works if life was a loop. Going back in time would suggest creating a new path, with a completely different direction. It maybe that you are the only one who knows the past, as you do re write the forthcoming history for everyone else.
So to me this is where the paradox falls down, yep killing my grand dad would then kill myself. So the terminator going back in time and killing the folks who will be fighting the rebellion does get rid of them from the future. But does it stop that path from happening? I just think that is the path that was meant to be and what it creates is the end of that particular path.
There are I feel many strings to time, and it which of those strings that we see or remember depend on which path we are on ourselves. Who is to say that if I did go back and kill someone in the past thus changing the future, that someone else didn't then go further back and change an event which prevents me from killing that person thus stopping my timestring from happening.
Also it does not have to be purely about killing someone, a simple interaction. I go back in time and talk to someone. Where previously I wasn't in that place at that time. So the person never had the conversation and then went off to do something else. There interactions cross over with other folks and then the ripple continues.
In conclusion I respect the thought behind the paradox but believe that any interaction with the past, would simply change the future and subsequent events but not stop the change itself from happening as that would be part of the path.
What would be your thought?