"However, you are very selectively choosing facts to draw a picture in which men "have the same amount of gender equality issues (maybe even more) than women"."

I'm not, really. Feminist discourse is based on the claim that women have more gender issues. They never really argue for that position. I've linked a list of gender equality issues (though my primary source is unfortunately not in English).

Here's a book on the subject if you're interested: http://granum.uta.fi/granum/kirjanTiedot.php?tuote_id=18450

"It is of primary relevance, because without properly understanding how we arrived at this point in history, you couldn't possibly evaluate the actual scale of gender disparities in social relations."

Yes you can. We can look at metrics for gender issues: e.g. do women get paid less or more (they get paid the same per hour), do women get raped more than men (not in USA), is the majority of violence made against women (it's about 50:50). It doesn't matter if women were discriminated against more in the past, if empirical evidence shows that they're not.

"what we do not need is more gendered lines being drawn in the sand."

Agree. Many men's rights activists agree on that point, and are against gender roles that hurt both men and women.

"Moreover, we do not have a social structure in which men's labor and sexual faculties are institutionalized in a form that is under female control, which would be a huge red flag that the pendulum has swung too far."

Your sentence implies that men's labor and sexual faculties are under male control, that's not true. Women decide who wins the elctions - majority of voters are women: http://www.bbc.co.uk/news/magazine-20231337

"One can advance equality and be vigilant against sexism, racism, and other forms of bigotry and discriminatory behaviors without resorting to more of this us vs. them bullshit that "men's rights" evokes."

That would argue that we only need men's rights movement, not a women's rights movement. Since the women's rights movement doesn't concern men's rights, we need a men's rights movement.

The biggest feminist organizations do not accept me as a member because of my gender. Their organization discriminates on the basis of gender. That's not equality. I cannot take part in the women's rights movement because of my gender. That's why we need a men's rights movement - so that men's gender equality problems are also taken care of. Currently 90% of the gender equality resources in politics is used for women's rights. That number should be 50%.

"In sum, a "men's rights" movement is not going to increase equality, because it is only going to codify more gendered division in the social fabric."

You make the implicit claim that men's rights movement is for gender roles. That's not true. In addition, you can use your own argument against women's rights movement, as it 'codifices a gendered division'.

"If you're really interested in enhancing equality as a social good,"

I'm really interestd in equality, and men's rights is the most important movement in recent years. Almost nobody used to talk about gender equality issues concerning men. In recent years, after the men's rights movement was formed, there have been small mentions of men's rights in official statements in the country I live in. Without a men's rights movement all the gender equality policy would say would be about women. Therefore, it's pretty clear that the men's rights movement increases equality.

I cannot link sources because they're not in English, but it used to be that only representatives from women's rights organizations were given representation in the official gender equality council of my country. They only talked about women's rights. Now a few seats have been given to the representatives of the men's rights movement.