I think Eobard accidentally erased the original Flash from the timeline when he killed Barry's mother. He shook up the timeline, erased the events that originally led to Barry becoming the Flash, and as a result he lost his connection to the speed force and got stranded in the past. By setting up the particle accelerator, and moving everything ahead of schedule to accommodate his needs, he probably views Barry as being his personal creation. Now he views himself as an integral part of the Flash legacy instead of the antisocial stalker we actually know him to be.
I like how he justifies his murders by telling his victims that they've been dead for centuries. "Nah uh, I'm not a murderer, you can't kill a corpse."