I couldn't help but poke around in here (no pun intended) and I came across this thread. Stop me if I'm not allowed to post here! I can definitely understand how this could be a touchy (pun intended) subject for some people, but I've actually thought about it to some length in a kind of philosophical way. We all have our own ideas about things, of course, and this is my idea about this subject. I'm not here to tell anyone that they're wrong or that I'm right. It's just what I think.
I don't think it has anything to do with control, or religion, or purity, or whether or not the breast, sex, and sexuality are "good" or "bad." Sure, it may have at one point, but I think it's beyond that at this point. If you ask, "Why do we censor breasts?" the answer is almost certainly going to be something along the lines of "Because they're sexy." Getting in to the matter of "Why are breasts sexy?" is a lot more difficult.
Sexualization of the female breast (and specifically, the nipple) is a kind of inherited fetish. Think about it.
I'm sure most of us are familiar and comfortable with the idea of things that are not particularly sexual being sexy. Spanking is a form of discipline, or abuse in some cases/opinions. Tickling isn't particularly sexual. Tying a person up with ropes and such isn't very sexual, either. But some of us find those things sexy, and some of us, indeed, fetishize and sexualize it. They are things that turn some of us on, and thus, they are often included in the context of sexual activity. Things we do with partners, things we do by ourselves, et cetera.
So is the game of "hide the nipple" we've been playing since Renaissance art went out of style in the same league as BDSM, then? Not particularly, but the two might be compared to show where the former is coming from as a fetish object.
Now, as for why this "fetish" is "inherited," I put it that way because we've essentially been censoring the female breast and nipple for several generations; long enough that we've really lost a grasp on the real reason why, and now censor it for the sake of censoring it. We're maintaining the status quo. In a sense, at this point, we find a woman's breasts to be sexy and sexual because the previous generation did. Really wanna creep yourself out? I'm basically saying that you can masturbate to the image of a topless woman (if you can, that is) because your parents could. And their parents could. And we can trace that, at least in modern media, all the way back to whatever person or group or artist decided "Hokay, it's time to cover these bad boys up."
In turn, if we stop censoring breasts and nipples, eventually, they might not be very sexy anymore. They might just be normal. Just functional parts of the female anatomy. Yeah, that wouldn't be so bad. But I'm not sure if I, personally, would want to live in a world where boobs aren't sexy.
Just my sleepy two cents.