"The genders are equal but not the same. To demand that we treat everyone the same is ridiculous."
The only response I can give is that we don't demand sameness - we demand that you treat individuals in the same way - as unique individuals. The ultimate pinnacle of the minority rights movements will be the complete eradication of sterotyping.
And don't you dare start arguing evopsych at me. Current sociological studies fall very short of sealing the nature-vs-nurture debate, and it is very clear to anyone who cares to look that many behaviors we take for granted as "male" or "female" are in fact imposed by society and not genetics (by the very telling fact that through our short human history the behaviors many people consider genetically gendered have swapped sides or weren't present before.)
Other things are simply irrelevant. For example, many people point to the difference in strength between men and women, as if to prove that, because the average male is stronger than the average female, the genders are destined to be treated differently. "We need men to do physically demanding jobs", they say, entirely ignoring the simple fact that there exist women who are stronger than the average man and men who are weaker than the average woman. Instead of defaulting to men being construction workers and women being school marms, perhaps we should leave the job allocation to individuals instead of broad groups, mmm?
Besides, the vast majority of modern society doesn't need to be physically fit beyond the most basic sense, so the point becomes more and more irrelevant. Intellectual and emotional fitness is becoming more important than physical.
Take any two individuals and look at their personalities (their true personality, not what they present to the world. This is key.). Contrast them with other individuals of their own gender and the opposite one. I would bet you that on average, the similarities between members of the same sex are of the same magnitude as the similarities between any two individuals of random gender. In other words, you cannot predict the personality traits of an individual by their gender.