Cultures - that making girls flat chested so they wont get married?

This answer will be part fact and part opinion. Historically, conquerours the wold over have raped and pillaged. Most adult men [except pedophiles ] want a female that looks at least a little womanly. Binding of the breasts makes the female look more childish , and hopefully less appealing . Some people in war time have even gone so far as to bind a girls breasts and cut off her hair and make her as grubby, smelly and scrawny looking as possible in order to avoid catching the eye of the enemy.

In my own family , after success fully dodging Nazi's , the Russians came, and the Poles thought they were delivered. My Great-uncle and cousin thought it was safe to go work the far fields. A neighbor boy came runnunig to my Great-aunt's house thru the woods, to warn her that the Russian Army was raping and pillaging even worse than the Nazi's because they had been starved on the front for so long they had lost all veneer of civility , and some, even humanity. With minutes to spare , my Great-aunt put my cousin under the kitchen floorboards, and when the soldiers came she opened the larder, said there were no men on the farm, and laid down on the kitchen floor right over her daughter and allowed herself to be raped multiple times , til the soldiers left, thinking they had taken everything there was to get. This is Motherly love , anything to save their daughter's virtue and prospects of a good marriage and better future.

I believe this breast-binding tradition can be found throughout history from ancient times to more recent history during the conquering of the Americas by Europeans. Mother love will sacrifice anything, up to and including their personal dignity or lives to protect their children.

As for breast-binding as a cultural thing, I don't know. I do know the Japanese used to practice foot-binding , thinking dainty feet signified feminity and gentility. The traditional Japanese kimono and obi does make breasts appear somewhat smaller, but I do not think that was the primary intent , just an unintended consequence of a fitted costume.