I think, despite some good points, you're mostly using linguistic tricks to avoid explaining anything, and ended up with a pretty unhelpful and unsatisfying position.

Firstly, some things are better than others. Generally, we prefer being alive to being dead. We think not being raped is better than being raped. You can't just throw all distinctions about priority under the "but that itself is masculinity" bus and be done with it.

Secondly, I don't think it's accurate that being competitive and figuring out what is better, even by small margins, is a trait so exclusively expressed by men that it should be called a masculine trait. I mean, sure, some misogynists would criticize Serena Williams' or Steffi Graf's drive to win as "masculine". This smacks of "only boys try to win races". Heck no! Girls like winning races too. And that's fine!

Thirdly, even if it were true that striving for being better than others was exclusively a "masculine" trait, rejecting it on those grounds would only mean that you reject both Reformer and Conserver and define all masculinity as bad. Maybe the Right should make fun of you. (Not the whole Left. Just you.)

Furthermore, while it's true that gender stereotypes have a tendency to get overblown, and also true that we excuse too many behaviors on the basis of gender, it is also true that there are very systematic differences even without strong cultural reinforcement--and as long as it's not actively causing problems, what's wrong with cultural reinforcement? We don't say, "Oh, Spaniards tend to like flamenco music...that's evil, we have to stop them from doing that!" It's fine! Differences are fine. Recognizing differences is fine. Insisting on differences to the detriment of peoples' lives is NOT fine. (Saying that the Japanese, or graduates of Harvard, or people with white hair are not allowed to like flamenco music is a type of evil.)

So your take-home message has a good part (yes, we indeed should recognize our common humanity first and foremost), but is ultimately unsatisfying because there is a thing to explain, and a thing to shape, and it you have not very successfully argued that all such distinctions must go.

If it turns out that men have higher levels of testosterone than non-men (however you wish to draw the boundary), and that testosterone is linked to aggression, then finding ways of dealing with that difference productively in a modern environment would be very important and rather man-specific. There would be nothing wrong with doing that. And what do you know, men do almost all have way higher levels of testosterone, and testosterone is linked to aggression.

And there's nothing wrong with labeling some of the productive ways to deal with that "good masculinity", among other things that deserve that label.