If you went back in time and killed your grandfather, would you still be born? Or did you just kill yourself?
The concept of time travel is complicated enough on its own without the possibility of killing a vital relative and negating your own existence. Even for time lords who aren't particularly interested in testing the limits of their own mortality by killing their teenage dad, things don't look great, because every time you travel back in time, you're probably killing off the previous version of yourself.
But if going back in time and killing your grandfather negates your own existence, because how coud you exist if your dad's dad didn't, do you just spontaneously vapourise the moment he stops breathing? How is that even possible?
No wait, don't try to answer this question on your own, I am here to help...
The first solution to this famous paradox is that when you go back in time to kill your grandfather, you're not going back to your own history, but a copy of your history, and everything you do in this version of your history will affect the alternate future of that universe, not your own.
Basically, if you go back in time and kill your grandfather, you don't exist, so your grandfather can't be killed. So there are two realities happening in parallel here. While all of this is 100 percent hypothetical, because no one's actually gone back in time to test this out, we do have evidence of two separate realities happening in parallel.
Supppse under that theory, if you tried to travel back in time, and changed reality in any way that altered your own past, it would create a paradox, so that reality could not exist. But in any universe in which that didn't happen, no matter how unlikely, you'd remain conscious.
Hence, from your perspective, events would seem to conspire to keep you from interfering with the past. Your time machine would break down, or your gun would jam when you tried to kill your grandfather, or maybe you'd have a sudden stroke and be paralyzed. Whatever it was, the universe would appear to resist the creation of paradoxes, because the timelines where it doesn't, you cease to exist.