Directly arguing has the downside that people with big egos will harden their positions even (or rather: especially) if they suspect they they might be wrong. If your goal is to let of steam while causing destruction, that is a valid strategy, if your goal is to reframe a topic, refute a point and/or win over the room, it often is not.
That all being said, we are talking about a public argument, not about private discussions. If you can make good points, bring the receipts arguing for those points is a good idea. However if given the chance it is a good idea to make these point in a smaller circle, in writing or in a one-in-one with your boss first, to give them the chance to agree with you when it is easy, instead of feeling put on the spot in front of everybody.