To find out
Here are some reassuring words straight from the American Cancer Society.
"We do not know of any epidemiologic studies published in scientific journals that suggest bras directly contribute to breast cancer risk or that lymphatic compression by bras might cause breast cancer. "
Another fact to chew on. If wearing an over-the-shoulder-boulder-holder was linked to an increased risk in breast cancer, statistics would have shown a drop in breast cancer diagnoses in the 60s when most women were burning their bras and going braless. But stats didn't drop.
So wear your push-ups, underwires, demi cups, and sports bras without fear, especially if not wearing a bra is not an option for your girls.