The entire world of A View from the Bridge is male dominated. As such, there's a lot of talk about what a real man is supposed to be like. The main character's ideas seem to be pretty traditional: big, strong, silent, hardworking. Things that he considers distinctly unmanly include: singing, sewing, cooking, and dancing. Don't get us wrong, the play doesn't champion these opinions. It just points out that they're there.
It's ironic that Eddie kisses Rodolpho to emasculate the young man.
In order to be a "man" in 1950s America, you had to maintain a certain level of dominance and power.