I don't understand what you are talking about when it comes to men. There ARE no requirements for men that are comparable.
And in the U.S., I would assume that our "struggle" with not wearing it is because of the culture. Women typically do not veil or cover their heads. When I first joined the charismatic church, I actually wore a headscarf for about a year. I got a lot of flak, ESPECIALLY from people from my church. Everyone constantly asked me if I was converting to Islam next.
I actually want to wear a scarf at the Orthodox church, but I confessed to my priest that I'm having trouble. First of all, I still struggle with dressing modestly. I know it's probably stupid to want to wear clothing that isn't modest, but I also like certain immodest styles. There, I said it. I wear modest clothes to church, but still just "don't feel right" about wearing the scarf. I also feel like it would be strange for me, as a catechumen, to wear it at a church where only a few women actually wear it.
I do not want to come off with a holier-than-thou attitude. My priest told me that when I'm ready, to just wear it. When I'm not self-aware and I have worked on the modesty issue, I will wear it. (I wear a small head scarf now, probably won't do the full one until I'm chrismated).
A large part of it is due to the culture in our country.
I know that I would be tempted to run around in the clothes that Muslim females wear in Egypt, Iran, etc, which I find beautiful. Part of me wishes that I could live in those countries so I wouldn't stand out as much.
"There ARE no requirements for men that are comparable." That rather begs the question of what is "comparable", doesn't it? I would say that, leaving aside what is culturally normal in everyday life, requiring (lay)men to be uncovered without exception, but allowing (lay)women to cover or not according to choice, expresses a kind of double standard in favor of women, does it not?
I assume what you are getting at is that in our culture, men are not normally required to wear hats in ordinary life, and in fact, most do not (at least not since JFK was president), so that in church, when men attend without head coverings, they are only continuing what is normal in their culture. Whereas women are not normally covered outside, so that when they are asked to cover in church, they are being asked to do something different from what is culturally normal.
All of this is culturally dependent, of course. And that explains the difficulty keeping the traditional rules in church, which explains why many pastors exercise economy in these circumstances. If your priest says it's OK not to cover your head, don't cover your head. Many in our church do the same.
However, none of this cultural contingency logically negates the notion that the requirement for women to be covered, and for men to be uncovered, is a part of Holy Tradition, sanctioned by the Holy Spirit. It is possible for something to be required by Tradition, but for economy to be exercised at certain times in recognition of the fact that in certain times and places it is more difficult to keep the traditional rules than in other times and places. Economy does not obviate the original standard.
Therefore, it is right for women to cover, regardless of what their peers are doing. Pastorally, I can see that sometimes it may be important to think about how covering one's head can lead to self-righteousness. But also, if one is abused for covering one's head, that could be interpreted as persecution for righteousness' sake. Only one's spiritual father can discern the difference.