This is based on the fact that soy contains estrogen and estrogen is a female growth hormone. However the type of estrogen soy contains is plant estrogen and cannot be converted into the type of estrogen which is compatible with the human body.
The problem is that soy isoflavones do not have the same MO as true estrogens, and are currently believed to be aromatase inhibitors. Aromatase inhibitors prevent the hormone androgen from turning into estrogen by inhibiting the enzyme aromatase. The majority of estrogen is produced by your ovaries during menstruation, however, the small amount you lose from the ingestion of aromatase inhibitors could potentially hinder breast growth, rather than encourage it.