The most well-known example of the impossibility of traveling in time is the grandfather paradox or self-infanticide argument: a person who travels in the past and kills his own grandfather, thus preventing the existence of one of his parents and thus his own existence. A philosophical response to this paradox would be the impossibility of changing the past, like Novikov self-consistency principle (if an event exists that would cause a paradox or any "change" to the past whatsoever, then the probability of that event is zero, thus it would be impossible to create time paradoxes).
https://www.indexacademic.ro/pdf/grandfather-paradox-in-time-travel/