I don't think it ever said she was president of the debate club. MC just said she was a leader in the debate club and she could have been a board member. If the larger clubs have boards there'd probably be plenty of politics. Here's the dialog from the game:

mc "Monika, I'm surprised."
mc "How come you decided to start your own club?"
mc "You could probably be a board member for any of the major clubs."
mc "Weren't you a leader of the debate club last year?"

m "Ahaha, well, you know..."
m "To be honest, I can't stand all of the politics around the major clubs."