@OneStep
I couldn't agree more as to the likelihood of it all stemming from before we were 'developed'.
I thought they had different image processing skills - I think men's eyes are better at spotting movement (a predator) and can focus on a specific spot whereas we're better at scanning. I guess where the joke (based in fact) comes from about men not seeing the butter in the fridge unless it's waving at them.
From this navigating back from a hunt, men also have more muscle mass, different skin, different hips making walking easier and they process calories more efficiently for more effort. Bigger and more efficient cardio-vascular systems. Testosterone lessens pain - good when skewered by a woolly mammoth - and adrenaline (men produce more) also lessens pain and lets you move further, more quickly and use your muscles more. It lowers your fear of danger as well as enabling fight or flight.
"But even if this is true, what good does it do us nowadays?"
The good it does us is that we function better as groups, families, cities, countries, nations etc when everyone's doing what they're best at. Specialisation is why humans have achieved so much. Because I don't have to worry about growing food and killing meat to eat, I do what I'm naturally good at and pay someone else to make my food. They pay me to make sure their children are educated. I couldn't do that if I was fixing my car instead of paying a mechanic and so on.
Girls should be encouraged to excel at what they want to do or what they're good at (hopefully the two coincide but that's an interesting concept in its own right) as should boys. They should have free choice and a level playing field but if innate differences mean one sex will likely be better at one thing than another then we shouldn't force a 50:50 split in the interests of fairness.
Fairness is bullshit and life isn't fair. Fighting for it is pointless and to me fairness is about equality of outcome; that's something no one with a modicum of intelligence should want. It's harmful to all involved.
What we need to do is judge each and everyone on their merits regardless of sex or whatever else. What's equally important though is misguided ideology where you're fighting and ignoring science so that you can hang on to your beliefs that boys and girls should have parity in all situations.
You speak about the changes that clothing (and I'm sure you include toys in that) can effect in boys and girls and I'm sure you're right. We can mould children, but should we?
Throughout the animal kingdom, children of different genders are played with differently. They're given different things to use and tasks to do. I'm not saying that we should mimic chimps for parenting tips but I do wonder if we're getting a bit ahead of ourselves and a bit arrogant to think we should change nature to suit our 'faith'* that boys and girls are the same if we leave them be.
tl;dr
judge everyone on their merits but don't get all feministy when males and females make different choices and achieve different things
*I chose "faith" quite carefully. The belief in something despite overwhelming evidence to the contrary. It also have great parallels with religion.