How does the term "Paradox" become the term "Paradox"?
Also, no matter what happens to your past, yu will ed up in the same way, with a different life.
That is how it is.
Say for example, you kill your grandfather, who is your father's father.
No worries, about you dying, you'll always appear in the end.
How?
Say you want to go to New York.
Yu can walk there, take the bus, or taxi.
From say, California.
You're grandfather is California.
You're New York.
Your father is Walking.
The bus and taxi are still available as extra options.
If you kill your grandfather by going into the past, it'd create a paradox that would, ultimately, destroy the universe. This is, technically, why time travel is impossible. Any step you make into the past would conclude that you've altered it with the future, and that its current state has now been influence by events that have yet to occur, leading to no source, and, again, destroying the universe. Unless you're travelling to a seperate universe with a different time frame. But, I'm still skeptical about parallel universes.
Even more so, if what we could travel in time, then the concept of time would have to be a particle recording device that recreates itself in seperate places at an infinite rate. Which, if looked at fundamentally, is ridiculous to consider.
Regardless, everything you said is not true. The chances of you being born, once the past has been disrupted, is very minute. Even if your grandparents were to perform intercourse, your father probably wouldn't have been the sperm cell that hit the egg.