What would happen if a guy travelled back into the past and killed his father, preventing his own birth?
Such paradoxes are often provided as thought experiments to prove the impossibility of travelling back in time due to the gross violation of causality.
It is possible to resolve it in some models of reality.
For example, we generally think of time as linear, but what if it had a branched structure? The "past" into which the guy travelled could be a separate branch of reality similar to his own past but not on the branch leading to the event of his travelling back in time.
Such an interpretation may seem fanciful, but there is a serious theory known as the "Many worlds interpretation of quantum mechanics" (MWI), that might allow such an idea.