I couldn't be bothered to read that last comment, but a paradox can also be something we can't fully explain. Sometimes it doesn't have a beginning, and sometimes it doesn't have an end, or both.
You could hypothetically also go back in time and kill your grandmother before she gave birth to you, but you wouldn't disappear. The only problem is that there would never be any records of your life, and you'd be stuck in a new timeline...
It would be weird if you saw yourself, and decided not to go ahead with it because it worked.
Then, there would two of you even though you never went ahead with it...
O_o