Matt's basically responding to the comments from the women trying to make it into a thing that men should be weepy & emotional in a regular way, and those chicks trying to hijack Archie's vulnerable moment (when he is clearly not a dude who goes around sobbing over every little thing) & leverage it into some feminist nonsense.
In that, I generally agree with his premise, but it's kinda clumsily presented.
Archie's moment resonated because it was obviously genuine, about something that should deeply matter to a man, & also clearly rare from him.