Hygiene quirks? Actually it reminds me somehow of the thread about peeing in the shower. I am sure that would be a deal breaker for some, but damn I love the freedom of flow... not to mention killing two birds with one stone. 
There are two kind of men: those who pee in the shower, and those who lie about it.
Honestly, I don't think anyone really cares about that, as long as you do it only when you are alone in the shower. If you're not, then... well. Don't.
Of course, the famous tradition. Basically you are saying anything that would be favourable to women is "equal rights" and "feminism", when it comes to exempts from burdens that should be eliminated for the true equality, then lets hide behind "tradition".
This is what in short ticks me off about the whole feminist movement. It's pick and choose whatever women want. No, I am all for equality, but I want it to go all the way and both ways for both genders.
No, I am saying that staying home after birth and getting kids upon divorce is is a thing caused by tradition and the fact majority of both men AND women like and want it hat way. In the case of companies/politics most of leadership positions are occupied by men, that's a fact. Cause is, again, tradition and prolly also that men tend to be a tad more ambitious.
So, you disagree or...? Not sure from your answer, to be honest.
You picked two examples, I told you what I think about them. So I don't see how can I tick you off by picking and choosing. I don't really see how the current state favors either gender in those areas.
No conscription? I mean... should I even comment on that?
Yes, you should.
Well, might vary from country to country, but it seems to be pretty damn hard to get to army even if you want to and that's only for administrative / supportive positions, for actual "soldier" it's harder yet, even impossible for some, so yes, it seems rather logical that there is no conscription.
There is also the mentality about army included. Which is another tradition, but eh.
It's not hard to get into the army. You get a letter telling you you're expected to be there at a certain date and then they don't let you out for however long you're supposed to be in it. The practice of only telling males they're supposed to be there is discrimination against all sexes.
.
Yes, but if you are a woman you don't get a letter and go, because first off, army doesn't want you in the army, which is somewhat relevant, then the army in most states don't really have any lodging & utilities for women at all. Even as voluteer you could have a trouble, because you need to be tall, for example.
So yes, sucks for girls who wanted to be a soldier and sucks for boys who never wanted to.
But this is historical (or as I said, traditional). Not too long ago, women weren't allowed on ships, let alone in the army, under any circumstances so... Progress?