Let's face it, in modern times a woman doesn't necessarily need a man to survive. With the invention of modern machinery, in-vitro fertilisation and stepladders we can care for ourselves. So what do I personally need a man for (except for that one thing, you know ... and sometimes not even for that...)?
But still, I don't believe in being supreme to a man on principles (although there are quite some men I feel supreme to when compared). Admittedly women do have some things men have not. We're usually living about 10 years longer these days (but get less money in pensions). We can give birth to children (but need sperm, whether through a donor or a loved one). We're better with so called 'soft-skills' or 'social-skills' (and usually less good with outright violence). And we don't keep our most vulnerable body parts - the ones necessary for children - outside our body. We can also endure more pain - or so they say - and suffer through more things physically as well as mentally. All those old and new arguments for the strength (or supremacy) of women aren't completely wrong. But they're not completely right either.
Yes, I don't need a man to master my life. But then, to be completely honest, I don't need a computer, a TV set or an internet connection either. Nevertheless I have them. The fact alone that you don't need something doesn't make the thing you don't need obsolete. If humans only kept things they really need, we'd still be living in caves and wearing fur and eating our meat raw. We need something to keep us out of the weather, we need food, sleep and human company. Apart from that, everything is optional. But then, we were never happy with what we had, that's why we don't live in caves and wear fur and eat our meat raw today ... well, most of us.
Yes, I know women possess a lot of the abilities modern society demands of us. That's mostly because today our society is no longer based on "strength", but on "knowledge" and "ability" instead. Those things were always important, but in the past "strength" surpassed them out of necessity. With modern machines it has lost that position.
And yes, a woman has to care for a child longer than a man, simply because we go pregnant for about 10 months (while the man theoretically is 'through' with it after a couple of minutes of sex). But our society frowns on men not caring for their children almost as much as it frowns on women not caring for their children (but the issue of not going to work after you've become a mother is another one entirely).
But what does all that have to do with "Female Supremacy"? Ultimately the whole 'job' every living being has in our world is propagation. And (even though I'm not doing that job and probably never am going to do it) to do this job, you need both men and women. And the more equal we treat each other, the better the whole thing will work. Just switching from men dominating women to women dominating men (not in a relationship in which both like it that way, but in general) isn't the right way.
So, what are men really for? They're here to share this world and this life with us. We're not supreme to them and they are not supreme to us. We're all created equal ... and there's no-one 'more equal' than the others.