You have to kill your dad?

Ben told Locke he had to kill his Dad if he wanted to lead the Others. Was that true?

We know that Ben killed his own Dad by gassing him. Richard asked him if he wanted to bury the body, and Ben said no, to leave him there.

I think maybe Ben made up that whole "kill your dad" rule. First, in order to kill his own dad, whom he hated. And then later in life, he stuck to that rule to try to keep Locke from becoming the leader of the Others. He knew that Locke wouldn't have the guts to kill anyone. He lied and told the Others and Richard that Jacob said that killing your dad is what "special leaders" do.

This would explain why Richard came to Locke and offered him Sawyer as a solution to his problem. (Back in the episode The Brig.) Richard even said that the Others were growing suspicious of Ben's leadership, so they must have known that he wasn't be truthful about Jacob's orders.

If I'm wrong, then I guess the Others just hate dads.