Who Taught These Kids to Debate, Anyway?

Yes, I coach debaters and as a judge once told one of my teams, "Debate IS a full contact sport."
I was bombarded today with their debate skills, just without their brains, hearts or forethought.
Here goes. I am particularly close to one of the board members (our system of captains) as she is friends with my daughter, she has been with me for three years and we are a lot alike. She tells me everything and helps me know how to relate to my teen daughter. It's like having a double agent...except she's not enemies with either side.
Evidently, some students have perceived this as favoritism and have developed jealousy. I can respect that. It's not intended and her grade is earned just like everyone else's, but I can see their perspective.
That's not the problem. The problem is one (or two) students took it upon themselves to start a petition to "reform" her or "remove" her from office for lack of leadership ability. Hello. This is NOT a democracy. We do not allow for impeachment. And have any of them heard the phrase, "Those who live in glass houses?"
See, they could all use their leadership skills more and I am there to help them LEARN...how to argue and how to be good citizens. It's all the same with me. What they did was petty and personal and that student was extremely hurt. They named no one else who could use a little "reforming" and even diminished her particular events.
Now the kicker. They actually offered an ultimatum that I do as they say or they will quit.
EXCUSE ME? Who has no leadership now?
I am so mad I could have a coronary on the spot. After two hours of conflict resolution, it turned out to not be as they had described. They claimed "everyone" agreed so imagine my surprise when student after student walked into class saying, "Um, Mrs. S, I have nothing to do with that. Why is my name on it?"
We've really got to work on our people skills, no?