What if a time traveler went back in time and killed his own grandfather before his grandfather had children?
This would make it so that the time traveler never existed, because he was never born.
This means that the grandfather never died, because the time traveler was never born to kill him.
This means that the grandfather had children, which means the time traveler was born, and so the time traveler did exist.
But wait, if the time traveler existed, he must have killed his grandfather, which means his grandfather didn't have children, which means the time traveler was never born... Example 2: The Bootstrap Paradox