The smartest developers and managers I've ever worked with are women. If someone is offended by being wrong or not being pandered to, this is not on you. I think the problems around this are firmly on the men and the culture that makes it untoward for them to listen and communicate effectively around or despite their emotions.
As a man, I can attest that I struggle sometimes with my ego around being wrong but facts are facts. When I'm wrong, I hope that I handle it in a way that doesn't make people feel they can't show me I'm wrong or that they have to wrongly agree with me or play dumb. Please don't. To me it feels like the best way to get this to stop is to just stop doing it. I know it's easy for me to say. Of course, assess the risks - maybe you have to back out of the persona slowly, but please do. We all gain from being genuine.
