Why is it private to see women's boobs ?

That is a cultural custom depending on what culture you are in. The American custom is not to uncover the boobs in public. But you can go to youtube and see videos from other countries with very different customs. In Brazil the tribal custom is to wear a chain or cord around the waist and nothing more. At the Moulin Rouge the dancers, dozens of them, are almost totally naked. In most of Europe it is simply a non-issue.