intuitively observed
This is the biggest problem. "Intuitive observation" means the evidence is anecdotal, and without "fine tuning." For example, you observe that in your experience women tend to be more social than men. My experience might be the opposite. And even if our experiences are the same, we can't assume that those differences are inherent. This is because many perceived differences between genders are actually due to socialization: women are expected to engage with others, to be subservient to others in a lot of ways, to be emotionally engaged. Men are expected to be self reliant and emotionally disengaged. This does not at all suggest a difference in inherent quality - it's due to society.
My major point still stands: the number of qualities that people have and their possible variations are practically infinite, and therefore immeasurable. Something immeasurable is unquantifiable. Thus, to say that there are more differences between genders than within individuals of a gender is an absolutely unprovable claim.
And you might insist on not being so scientific and relying on your anecdotal experience, but these ideas have profound impacts on those around us. Thus we have a responsibility to others to examine these biases and ideas with a fine toothed comb