I'm not sure if this is supposed to a rhetorical thread, but I'm going to try to answer a few anyway.
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Why is it socially acceptable for men to walk around shirtless but not socially acceptable for women to do the same?
Western society has the idea that a female's breasts are sexual in nature (even though there is no direct link breasts and the act of intercourse). A man's chest isn't seen as sexual. So, our society has generally agreed that they should be covered up in public (just as one must cover one's reproductive organs, as they are sexual in nature). I don't know the origin of this belief. The interesting thing is that (I think) the primary reason that a bare breast is a object of sexual arousal for men in western society is because it's always been covered up! So it's kind of a chicken and egg situation. Compare this with many non-western cultures (like in Africa), who think it's totally normal for both men and women to walk around with their chests bare.
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Why is it socially acceptable for women to wear skirts but not socially acceptable for men to do the same?
I don't know this all that well.. but here's what I remember hearing. In Ancient Rome, everyone wore skirts. No one wore pants. The only people who wore pants were various nomadic tribes. They wore them because they made riding horses easier. In these tribes, both men and women wore pants. It spread amongst the various tribes but not to Rome.
So now we're getting into the fall of Rome and entering the middle ages. All of this stuff I'm about to write takes place over a long time period. During this time, social class is becoming more stratified (surfs, merchants, land owners, knights, kings, etc..). Knights started to wear pants because of their utility in riding. Now, the men that were in nobility eventually started to wear pants in order to copy the knights - knights were badasses and the noble dudes could safely emulate them because they had power over the knights.
Here's where it gets murky, but clothing is now taking on an additional role of signifying class status. So you can tell where someone's position in society is just by looking at them. Somewhere along the way, it became guys = pants only and girls = skirts/dresses only.
Much later.. women were able to make "women wearing pants" socially acceptable, but men have not yet been able to make "men wearing skirts" socially acceptable
I know that's kinda vague and ill-informed, but that's all I got!