"Private areas" are not special. They act as a way of survival, just like every other part of the human body. I mean, all breasts are are a piece of fat and yet, men and woman think of them as "sexual". No, breasts produce milk for infants. They are not intended for sex. Sure, you can play with them during intercourse, but really, they are just like udders on a cow. The same goes for the reproductive organs. The reason people like sex so much, is because it's meant for making babies. It feels that way because you're supposed to like sex.
Human reproductive organs are body parts...As are hands, feet, arms, legs, neck, face, etc. There is no legitimate reason for any part to be private. If there is, I do not know them. Seeing a penis is the equivalent of seeing a hand. There is no harm to it. They are both body parts. If anyone wants to explain to me why it makes sense, please feel free to.
Human babies have small heads, hence small brain, hence underdeveloped brain at the time of birth.
Brain grows till you're 16.
So extensive care is required by mother to her child for a long time compared to other animals.
So Mother needs to reproduce less and care more for her already born child(s).
This led the inception of the Dresses.
Dresses prevent arousing men all the time, thus reducing the reproduction rate of females.
Things like a reproductive organs, bums, and breasts excrete liquids so I can see why they are considered off putting and private to most. Defecation, urination, sex, and breastfeeding, whilst natural are disgusting to look at for most people. That's why people cover up. It's to cover up their modesty. Also it's folly to assume all ordinary reproductive organs are all look perfectly pin up. When people grow old quite frankly their bodies and dangly bits look repulsive to be honest. Only young people have pert bodies so it's important to bear that in mind. Not everyone looks great underneath their clothes.
This is a very intriguing question, and I suppose in a way it's right to say that reproductive organs are just body parts the same as hands and necks (which people are happy to show in public). On the other hand, it's more what the organs are used for that is considered private (sexual intercourse, relieving oneself etc.), and just by extension the organs themselves are 'private parts'. As human beings, our intelligence has led us to develop emotions such as embarrassment, as well as an acute awareness of what other people think- something no other animal has. Cave people walked around with no clothes on, but they also didn't attend school, have any laws or linguistic skills. Modesty is just another part of evolution.