The phrase "you can't run with the hare and hunt with the hounds" means that one cannot support two opposing sides or ideas at the same time. Some synonyms for this phrase include "you can't have your cake and eat it too," "you can't sit on the fence," and "you can't have it both ways." All of these expressions suggest that one must choose a side and commit to it, rather than trying to please everyone or take advantage of both sides. It's a reminder that true integrity requires making tough choices and sticking to them, even when it's not the easiest or most popular decision.