[brainfire]

Talking over a woman who is speaking for herself, and discussing whether she is competent without her input, is a classically sexist way to be rude.

[zakk]

No, it's not, someone is simply rude and talks over everyone. A rude person will talk over men, women (without being sexist), black people (without being racist), etc.

Either you demonstrate that the arrogance is specifically targeted towards women and because they are women, or you cannot speak of sexism.