Sometimes working for a company is like being in a relationship. You don't want to be always right and state it. This could affect negatively your position in the organization structure, unless you decide to take the hard path and become a change culture captain.
When you know there will be a messy meeting and there is nothing you can do about it, the best thing to do is to avoid it. Messy people produce messy meetings, and they take the time and the energy of everyone who is part of it. That is why instead of being part of this drama, find a better team and better meetings to invest your precious energy.