I'm not sure I buy your premise: firstly, the degree and form of male-female differentiation in social roles has varied widely across time and culture in human history so I doubt it forms a uniform evolutionary driver such as you describe. Secondly, the degree of male-female differentiation appears to me to be much greater in species such as gorillas, lions and peacocks than it does in humans so I'm not convinced that humans would stand out on this front as a species we'd expect to have greater genetic differences.

Even so, the only genetic difference between male and female humans is the Y-chromosome. The X appears in both males and females and doesn't have exclusively female lineage so it can't acquire separate genes for male and female. The Y chromosome contains very few genes so its not capable of manifesting a major genetic gap and because there is no recombination in the Y chromosome it is not a fertile ground for new genes anyway.

So males and females have essentially the same genes. However, this isn't the whole story because how, when and whether genes are expressed is about as important as what genes are encoded anyway. It is these differences that enable big differences between the sexes not actual coding differences. 

Are human males and females more genetically different than members of other species?
I remember reading once a very clever analogy, which I was sure that I had found in the writings of Yeshayahu Leibowitz (who sourced it, from memory, in the writings of the Rav, R' Yosef Ber Soloveitchik, who himself sourced it in the Rambam), but I can no longer locate it at all. In essence, the analogy stated that God is like fire. Different objects, when dropped into the fire, react differently. Some become hard. Some become soft. Some let off smoke. Some change their hue. Some make a noise. Some might explode. But while all of these different reactions can be found, at no stage is the fire anything other than a fire; the difference in responses to it is to be found in the different objects that come into contact with it.

So too, the analogy concluded, when it comes to our relationship with God. When we pray, we change ourselves in order that God might interact more favourably with us. We do not hope for God to change in any way, but for ourselves to change instead. God's influence upon the world is constant and unchanging; it is we who are in flux.

Does this analogy sound familiar to anybody? If you can direct me to a printed source (be it in the writings of the Rav, or Prof. Leibowitz, or whomever it was who came up with this), I would be much obliged.
