If you have ever read a short story, novel, poem, or piece of speculative fiction about time travel, if you have ever seen a TV show, movie, web short, play, or commercial about time travel, if your physics professor ever mentioned time travel in class, you know the most important rule: don't change anything in the past.
If you change something in the past, even something totally insignificant -- like, say, giving Native Americans safety pins or encouraging Napoleon to grow a beard -- you will return to your present time only to find that it has transformed into a nightmare world, where Nazis have teamed up with Martians to enslave lesser races and turn them into hamburgers. If you somehow travel into the past, you must make sure that your presence there is totally undetectable, that your arrival and departure create no ripples in the fabric of existence, that you change nothing. God forbid you should somehow prevent your parents from meeting, or from getting married, or anything like that -- you will wipe out your own existence!
Except that, if you wipe out your own existence, there will be no "you" to interfere with your parents. Which means that they will meet and get married and have you, and you will be born.
Which means that there will be a "you" to interfere with the past, wiping yourself out of existence.
Which means that there will be no "you" to interfere, meaning that everything will unfold in exactly the way that it already has.
Which means that you will be born.
Which means that there will be a "you" to interfere with the past . . .
The problem with interfering in the past is NOT that it would change the rest of the course of history, necessitating a trip back to set everything right (hilarity ensues as the hero finds himself fending off advances from his own mother!). The problem with interfering in the past is that it would create a tear in the space-time continuum, and send you rocketing back and forth between existence and non-existence like a metaphysical tennis ball. Plus, remember the butterfly effect: if your parents had never met, obviously you wouldn't exist, but what else might have changed? Who would they have married instead? Would one of them have found the cure for cancer? Would one of them have become the next Hitler? Imagine a world of constant, rippling change, where you rocket back and forth between existence and non-existence, the whole face of the two worlds drastically different. One world would be the one we know, but what would the other one be? Utopia or Hell?
Which is a fascinating concept for a story.
We all assume that life proceeds onward in a straight line, unhindered by any science fiction tropes. But in reality, there was a time traveler at some point in the past/present/future who so badly fucked up that the entire universe is constantly being re-created and destroyed. Every generation, the re-set button is pressed, and none of us are aware of it, because we are all living inside the loop (Matrix-like). There is no progress, no moving forward. Just endless, senseless reincarnation. And physics.