Grandfather paradox: The paradox proposed to discount time travel and exhibit why it violates causality. State that your grand-father makes a time machine. In the current time, you employ his time machine to go back in time a few decades to a point before he married his wife (that is your grandmother). You meet up him to talk about things, and an argument results (presumably he does not believe that you are his grandson/granddaughter), and you by accident kill him.
When he died before he met your grandmother and never had children, then your parents could surely never met (one of them did not exist!) and could never have given birth to you. In adding up, when he didn't live to make his time machine, what are you doing here in the precedent alive and with a time machine, when you were never born and it was not at all built?