I like it - very funny!
One thing that allowed us to leave caves was the ability to adapt our thinking, language and culture to new enviroments, perhaps that would be a good thing to be remembered by both sexes!
On differences between men and women, I think they are overplayed. We share a huge amount, so much that it becomes hard to focus on, which is why I believe the differences become the focus. I imagine the balance between similarity and difference is roughly equal in proportion to our genetic similarity vs difference between us.
Then there's another interesting point, in artificial intelligence research they found that placing instinctive 'drives' in AI units was hugely unsuccessful, and yet the more basic the intelligence of a life form the more that life forms behaviour is governed by it's genetics (less adaptable, less individual, less flexible). the problem was AI hadn't yet created forms intelligent enough to overide 'instinct' when needed - not even as clever as real bugs! The more complex the intelligence of a life form is, the more able it is to have executive control over it's 'genetic' behaviour - it can chose to migrate to escape a cold winter - or to stay, it doesn't fly east in response to an automatic body clock!
As humans we have exceptional abilities to go beyond behaviour written purely in our genes - think carefully about what you're doing right now, reading this, this forum, a woman's response, a man's post, a discussion...
We don't live in caves anymore and we are adapting - watch this space.