Question about Paradox's?

There a several proposed paradoxes concerning time travel, a paradox within itself is a concept not an actual thing. Still, thinking of perhaps the "Grandfather Paradox" which describes a man traveling back in time to kill his grandfather before he or his father was born. The idea is that how could he kill his grandfather when in doing so it would stop the process leading to his existence, and thus his time travel to kill his grandfather. The one proposed way that paradoxes are avoided is through the idea that time travel backwards would take you to that time in a parallel universe, thus the grandfather you kill really isn't your grandfather but the grandfather of another version of you. Essentially though, a paradox itself prevents its own happening by definition. It describes an impossible situation.