All cultures have rites of passage. I couldn't imagine a stronger way of accepting a young woman into a woman warrior culture than by cuttign one breast off. Think of the symbolism. I'm sure the folks who thought up the mythology did, eh?
I've always understood it to be a practical sort of thing rather than symbolic. And not every culture is as fixated on breasts as ours is.
Anyway, the Amazons may not be myths. At least not entirely. I like the theory that they were woman who had to 'defend the store,' so to speak, while the men were away at war, and the Greek who came upon them got the wrong idea. If he was an Athenian, I can see why.
rites of passage can be as simple and as complex as you can think of circumstances to arrange them around. The Amazonian women are supposed to have been somewhat based on a real events. There is evidence that of a cult of the woman warrior as well. A rite of passage can happen at any stage of life, signify anything. Functionally it marks the passage of someone into a society or part of society where they are expected to change their behavior in favor of the new group. So you could see a young girl having this rite of passage to mark the end of childhood, or simply to mark to her community that she will become a warrior. Keep in mind that the bows commonly used throughout human culture are not the massive English longbows of yew. A boy began to train at a bow like that as a small child--it took a lifetime to become a master. Most bows aren't that damned serious. A month or so and you can be expected to become and average shooter. Most bows are in fact skinny little dinky looking things and they're used with multiple pronged arrows for killing small game. Not to hard to scale up from that to a leve tah tcan kill a person without it being a big switch.
"They have no right breasts...for while they are yet babies their mothers make red-hot a bronze instrument constructed for this very purpose and apply it to the right breast and cauterize it, so that its growth is arrested, and all its strength and bulk are diverted to the right shoulder and right arm." Hippocrates
Now, there are a number of sources about them, and few agree on fine details. But in general there seems to have been a culture where rwomen were set on a level playing field with men (at least a level playing field) and they seem to have been expected to hunt and fight as well as thier men. In fact, if yo look at today's culture, it's quite similar to what the Amazons were described to be like.
Now, if you squint a bit, and take away what was probably made up (Hippocrates wasn't there and didn't have a direct source--and ancient authors were notorious for making up what they didn't know) or and base it on what we know about cultures, it is entirely possible that this was actually a rite of passage performed in girls to signify that they were expected to join the ranks or begin to study to join the ranks, of adult women in their culture.
I recently had a sinus surgery. They drive a needle about the size of an iv needle into your sinus and heat it up to 300 degrees. This cauterizes the sinus and shrivels it up, allowing you to breath through your nose again (I've had my nose broken a lot and although it's been well set it left me with issues breathing) so the cauterized breast make sense to me. I'm not sure doing it anytime before puberty wouldn't be effective. So maybe as soon as the kid starts to bud they burned her with a ceremony. And of course, all cultures see the breast as a sign of motherhood, if not sexuality. So cutting one off would indicate a strong notion of what women are supposed to do with their lives, eh?
All of this is suppositional of course. And only barely has anything to do with real live titties. But it's an interesting idea imo.