Since we are talking history - with some search - I found out that Person1 has recently put out a #metoo experience and called out some incidents at Caltech. Don't you think there's not even a little bias here against every possible "person2" who happened to be a male and just gave a technical feedback? Not like that's an invalid statement. He does have valid points in what he said(just the way he said it might not have been ideal). But it escalated very quickly!
The more professional approach is to simply present one's case without commenting on the quality, style, or manner of the other's presentation.
My two cents, best of luck in your studies :)