Looking back I find I did actually post something about this a few months ago, but let's go again. I could have been clearer then and I'll try to be clearer now.
The argument here is that breasts are what I'll call a sexual display; that is, a display which evolved for the purpose of attracting sexual partners.
Most sexual displays in the animal kingdom are on males. Think peacocks fanning their tails, bullfrogs croaking, moths emitting pheromones. In various ways they communicate to females the message "My genes are a good reproductive investment for your genes".
At this point I need to pause, because my readers have different levels of education in biology and some of you might need a refresher on what natural selection is and (more importantly) what it isn't.
For brevity's sake, when we talk about evolution, we nearly always have to use language that sounds like we're talking about a conscious agent with goals, values, and purposes. We say "Giraffes evolved long necks to eat leaves from the tops of trees", as if that was something the giraffes wanted to do and made a plan and executed it; or else we say "Giraffes' long necks are meant to let them reach the tops of trees," as if we were invoking some higher designing agent who had purposes in mind for what they wanted giraffes to be.
Neither of these things is how it works.
Giraffes evolved long necks because, for a significant period during their evolution, giraffes who could reach higher leaves consistently made more baby giraffes than giraffes who could not.
It doesn't imply a binary; we don't have to suppose that shorter-necked giraffes had no babies, only that they had consistently fewer babies than longer-necked giraffes. That way the genes involved in making long necks became more and more common in the giraffe population.
The short way to describe this is to say there was selection pressure on giraffes to grow longer necks. Selection pressure is a term I will be using repeatedly.
So when we define a sexual display as a display that evolved "for the purpose of" attracting sexual partners, what that means is that there is or was selection pressure on that animal population to attract more sexual partners.
Now in many animal groups, notably including mammals, the selection pressures for sexual partners are different on the different (reproductive) sexes.
If a male placental mammal mates with five females in twenty-four hours, the maximum number of pregnancies that can result is five. If a female placental mammal mates with five males in twenty-four hours, the maximum number of pregnancies that can result is one.
That's why there are so many more male sexual displays in the animal kingdom than female ones.
At this point I need to stop myself from going down a gigantic sidetrack about why none of this implies that the sex binary or the gender binary (or the gender-sex binary) is real or natural. Intersex individuals exist in all sexed species.
We are not the only species in which social roles correlate with reproductive sex but some individuals cross the gap and self-socialize into a different-sex role. We are the only species that has ever been observed to try and prevent individuals from doing that.
OK. Sidetrack averted. I can talk more about that if anyone wants to hear it but maybe not on this thread.
Female sexual displays do exist in the animal kingdom; there's just not as many of them. Before we started routinely desexing our pets, female dogs and cats were notorious for the olfactory displays which would draw males of their respective species from all over the neighbourhood.
This implies that there is or was selection pressure on female dogs and cats to attract multiple males; not because they can get pregnant to multiple males (they can't), but presumably so they can have their pick of the best males.
But human breasts are not sexual displays, and I think we have the pieces together now to explain why not.
Female sexual displays, at least in placental mammals like cats and dogs and us and chimpanzees, are generally fertility advertisements. They start when the female is fertile and stop again when she isn't.
Human breasts, it need hardly be said, do not swell up overnight and then shrink back to flat one week later when their owner's menstruation starts.
But our closest relatives, chimpanzees and bonobos, do have a body part that does exactly that -- not their breasts but around their vulvas. For one week of the menstrual cycle, it looks like they've sat on a bright pink balloon and got it stuck to them. Gorillas have this too, though theirs isn't quite as blatant. And yes, this is extremely sexy to the males.
This is almost certainly something that they've all inherited from their common ancestor. Who was also our ancestor, because we're more closely related to chimps and bonobos than gorillas are.
Which means that, at some point in human evolution, this was something we lost.
When females of a particular species have a fertility advertisement, this is always going to place selection pressure on males to pay attention to that fertility advertisement. Males that ignore it are not going to have as many babies as males that pay attention.
Therefore, if there is any selection pressure on females to attract as many males as possible, those females will certainly keep, and probably enhance, whatever fertility advertisements they have.
We didn't. We did the opposite. We lost ours.
Therefore, there cannot have been selection pressure on female humans (or proto-humans) to attract multiple males.
Therefore, female proto-humans cannot have evolved any feature for the purpose of attracting males. Not even boobs.
Which is pretty much case closed, but let's just put the tin lid on it.
In other placental species, the breast distends during pregnancy and stays distended during lactation, after which it returns to a flat state.
Placental mammals can't get pregnant while already pregnant. Lactation suppresses fertility too, though not reliably enough to be used as a contraceptive.
This means that in all other mammals besides us, distended breasts don't say to males "I am fertile right now, fuck me."
They say "I am not fertile right now, don't fuck me."
There is no way in hell this could have become the basis of a sexual display.