I believe it is referring to the fact that most of the men who post about their bettas seem to have a soft spot for them and it is perfectly manly. The bettas themselves are very handsome little men and would not in any way be mistaken for girls (sometimes even the ladies are little tomboys) and they are quite affectionate towards their owners at times too.
I started something in another thread without meaning to and then again here. To try and explain what I meant...
Some men are really sensitive and caring and don't have issues with expressing emotion (women are notorious for emoting). Some men are quite the opposite and to talk to a 'fish' wouldn't be a 'manly' thing for them to do.
I love men that are sensitive and freely emote and don't worry about society's ideas of what a 'man' is. You guys have such pressure. You know, big boys don't cry and all that. To me, big boys who cry ARE men. Make sense? I'm enjoying seeing men enjoying their Bettas so much.
Men enjoy fish keeping just like they enjoy pet dogs or lizards. I think men who try to be macho to hide their soft side are insecure. I find that having sisters helped me understand women a lot better than the average man.