This is the famous grandfather paradox.
Let's say that the time traveler goes back in time a hundred years and kills his grandfather when his grandfather is only a little boy. What happens?
On one hand if the grandfather was killed when he was a little boy, there is no way he could have been a grandfather, and so the time traveler could not have been born. On the other hand if the time traveler had not born, the grandfather would not have died....