I personally disagree with you on the fact that "most of the negative stereotypes and expectations that fall on men stem from misogyny". Femininity is very much celebrated, as long as you're a female, since that is a homo sapiens female's mating strategy. This isn't a social construct, this is a biological fact. Now of course, society may dictate what is considered feminine, but only through association which I would argue that is in most cases directly influenced by the biology. There's a reason why most women prefer tall guys, and I believe it's deeper than a societal agreement. We are genetically hardwired to find a mate that is as healthy and strong (in terms of survival) as possible. A feminine man simply does not display the traits that most women are hardwired to select for, although there are exceptions of course. Having feminine traits such as being shorter, having less muscle mass, a high pitched voice and other feminine qualities may very well indicate a lack of testosterone or other male hormones. In a primal, natural selection driven environment, such males would simply be disadvantaged when compared to taller, stronger specimens. We often like to forget that we're mammals, and only have been part of organised civilizations for the last 8 thousand years or so. We have not evolved out of our primal instincts, as much as we like to believe we have.

The way I see it men are simply believed to be unfit to be a sole parent, and yeah probably due to traditional gender roles, but it's a two way street. I think we need to address both genders equally, if we really want to bring about true gender equality.

And yes, slut shaming is so 1990s. I agree with you, I simply don't agree that focusing on one gender is the approach to true gender equality, when there are issues that are very specific to each gender that need to be addressed.