The Grandfather Paradox is the leading argument against time travel. Basically it is this:
"suppose a man traveled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension, the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which in turn implies the grandfather would still be alive, and the traveller would have been conceived, allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox."
At first glance, it appears that this debunks the myth, or possibility of the creation of time travel. You read that and go "there's a point" and you move on. But something just doesn't seem right about it. At first glance, I can't figure out what it is. Then it strikes me... This is all if we assume that life runs on a controlled path. That life is predetermined. Is it? To be able to look not just back, but into the future, life must be predetermined. You can't go into the future if the future is the unknown, or the result of the daily actions of your life. If that's the case, then you've got no control whatsoever over your life and every decision you believe you are making has already been made for you.
That's kinda fucked up. It's also impossible to resolve so I guess there's no point in dwelling on it.