How time travel paradoxes are really avoided
The physics of relativity as worked out very successfully by Einstein shows that space and time are linked mathematically as a 4-dimensional manifold called spacetime. This strongly favours the tenseless view of time in which not only is 3-dimensional space a permanently existing entity but so too is time. That we experience the moment called "now" which seems to move through the 4-dimensional manifold as a dividing line between past and future is not something described by the laws of physics but this concept of a block view of spacetime as something existing permanently is clearly believable.
This view of space and time encourages speculation that it may be possible to explore time in a different way from the automatically progressing "now". In other words, that time travel may be possible. No known law of physics prevents such travel.
Philosophers have written at length about the paradoxes that would result from time travel. The most famous one is the grandfather paradox: what would happen if someone could travel back in time to meet their grandfather before he had any children and murder him?
All such discussions ignore an obvious reason why such a meeting would be impossible. The point is that it is not just a matter of travelling to a different time. The requirement is to travel not only in time but through 4-dimensional spacetime from the present location to the grandfather's time and crucially also to his position. Meeting would only be possible if the position at the earlier time could be reached. This really is impossible because the Earth is moving at a very high speed through space: at more than 11,000 km/hr in its orbit around the Sun which in turn is moving at 1,300,000 km/hr relative to the cosmic microwave background (a plausible reference frame for the known universe). Locating grandfather's position in space at any given time during his life is clearly impossible, and consequently it is impossible to move to the right position, regardless of any travel in time.
So how does nature avoid the philosophers' paradoxes? By keeping everything whizzing around. If we could travel in time we would almost certainly perish in the vacuum of space.