Why should women try to be a man's equal?

Out of many random things that irritate me, one which ranks high are people who cry over their rights. I believe there is a balance in nature - you do your duties well, you'll be awarded with your rights. Too ideal, yes, but that's how nature is, isn't it? Ideal to the core, but as simple as it can get. But then, the human beings that we are, we fail in doing the simple things most of the times, then we grow a complex within ourselves, and then we demand our rights, for we know we aren't going to get them on a silver platter since we haven't done our duties well enough. 

I've heard about various organisations which demand rights - animal rights, human rights, gay rights, women rights, etc, etc. I am too naïve to understand why these organisations are required, but there are certain concepts that they preach, which I find silly. To start with, most of the woman rights arguments revolve around the fact that women are to be treated equal to men, because they in fact can do anything that a man can. I agree the world is a bit male dominated, I agree that women can do anything that a man can, but I do not agree that women need to be a man's equal. I've been touted as a 'male chauvenistic pig' by a female friend of mine, and she says so whenever I point out to something that any woman tries to do which is not actually required.  I say so not to degrade women, but to make a point that, it is not something which is needed to prove that they're as good as men. 

I have a lot of respect for women. What better a person to know than my mother, who I respect for how she brought us up (for such amazing children, you got to respect her, no?), how she holds the family together, how she does so many little things, each day, I can only dream of. I've witnessed a sister so brave, I'd shit in my pants each day if I was her. I've seen how a woman can love, makes me think I am a nomad when it comes to loving someone. Point being, there are a lot of things that women can do, which are in a way far more superior than what a man can imagine doing. They can do household chores at ease, go out there and do much better than a man when it comes to having a career, and above all - love unconditionally. 'A man can never be a woman's equal', I had read somewhere which I can't agree more with, and I keep wondering when woman are so much more superior, why should they try and degrade themselves to be a man's equal?