Very often when two people have an argument, they go to a third person and ask him to be a judge. If the person is timid and is afraid to take a decision, he will end up saying that both parties are in the right. He will support both sides of the argument because he doesn’t want to hurt the feelings of his friends; sometimes, he does this with an ulterior motive in mind. This desire to be on friendly terms with both warring factions by supporting their arguments is what we mean by the expression, “running with the hare and hunting with the hounds.” The individual is trying to be both the rabbit (hare) and the dog (hound). He wants to be the hunted as well the hunter; and this is just not possible. This idiom is considered rather old fashioned.
Examples: Latha is a very clever person. She runs with the hare and hunts with the hounds.