Nobody really likes it, but half of the "politicality" of management has to be set in place to allow people to communicate with others who may or may not suffer from a sensitive ego and the company hasn't had time to figure it out yet. On top of that, it's usually a judgement call and may be a poor idea to formalize into your process an escape hatch based on judgement.

So maybe the original mistake was from the manager who presented a sensitive idea without enough seriousness to induce a careful response. Or the op who was too quick to feel comfortable interpreting it as a joke in what turned out to be a serious meeting. Or the culture which enabled the terms of the meeting to be ambiguous to begin with.

Only after that can you get into things like speculation on the maturity of the manager. It's actually quite a high maturity bar to jump over to stomach being laughed at by an expert. Not saying you can't set that as a goal, but merely that you ought to think about what happens when you find yourself dealing with someone who hasn't met that expectation.

At that point, the damage was done. I tried to explain why her approach of changing N things simultaneously wasn't more efficient than changing N things sequentially because of the combinatorial explosion of interactions, but she wasn't technical enough to understand what I meant by that, which made her angrier, and when I suggested an approach that would give us a temporary "Plan B" just in case we "ended up a couple of weeks late", she declared me "unsupportive" and ended the meeting.