Time travel seems impossible. It would imply that you could go back in time and kill yourself in the cot. If you do that then it is impossible for you to be able to kill yourself for you are already killed. A contradiction arises.
You are just you. You reversing your existence would be nothing major.
But what if Jesus Christ, a major figure, went back in time and strangled himself in the manger?
A contradiction is a contradiction. It is not about how much impact it has.
But let us bring some psychology into this.
Despite how logically a contradiction is just a contradiction, our emotions and our socialised side will treat the murder of baby Jesus as a bigger contradiction than your ceasing to exist.
Some mystics say that though we cannot bodily travel in time, our awareness does travel in time. They say the past and future come together to make the present and this makes the past and the future the same thing. If so, my memory is the reason why I think that time is consecutive.
But they overlook the fact that if we cannot travel back in time physically, then we cannot do it mentally and yet in reality either. If I thought of an apple on 21 September 1997 at a certain moment, I cannot change what I thought of now.