What Woo-Moon knows: Muncheon are arrogant fanatics who looks down on all other martial artists and plan to destroy them, until Muncheon is the only martial arts group left standing in all of murim.
What Woo-Moon says: This is only about my revenge, nothing else. It's personal. I must destroy those Muncheon guys after what they did to my grandpa and junior sister.
Either the guy is a blistering idiot or there's some weird code of honour that forbids him from saying that destroying Muncheon would be essential for all the other martial arts groups. You can't even blame the matriarch of the Frozen Palace when Woo-Moon insists that this is nothing but his personal revenge, which he can't handle alone and thust wants to drag others into it. Otherwise I'd, indeed, say the matriarch is a greedy, selfish fool who doesn't know what's best for her own people.
As it is, he should forget the whole place. They aren't really a suitable ally since they don't seem to possess any interest in fighting Mucheon. Chances are they have ongoing deals with Muncheon. After all, we do know that although Muncheon is planning to eventually destroy other martial arts groups, they aren't above using them for their own purposes in the meantime.