We can agree that disagreement doesn't have to be dismissive or sexist.
But yours was dismissive and a little sexist.
Being rubbed the wrong way is a common expression. Although it references an animal's fur being rubbed the wrong way, we dropped the "fur" in common language years ago once rwfereinf to women or women's body parts as animals or Castorid pelts became common because of the allusion that then made.
I have never heard the word fur thrown in there in my entire life and I am not young.
Your argument about perception is both a cop out and dismissive again.