Somatotropins (growth hormones) are not the same as gonadotrpins (sexual development hormones), and they don't cross functions, especially when applied to different species.
Why is puberty coming earlier for girls today? @ HowStuffWorks
...this hormone isn't a steroid like estrogen, and it's destroyed too quickly during digestion to have any real effect on the human reproductive system. Right now, the biggest culprit seems to be the super-sized American diet. The rate of obesity in children ages 2 to 11 has nearly tripled over the last few decades [source: CDC]. Fat cells produce estrogen, as well as the hormone leptin, which can stimulate the release of the hormones that trigger puberty.
The truth behind early puberty @ Livescience
On average, African American girls show signs of puberty, with breast development and chemical changes in their bodies, almost two years sooner than white girls, at age 8.8. This is according to the largest study on precocious puberty, involving over 17,000 girls, by Marcia Hermann-Giddens of the University of North Carolina, published in 1997 in the journal Pediatrics.
So it's not the milk and it's probably the fatty diets, though we can't rule out pollution from plastics in some cases. And based on what I know about the regrettable history of women and the medical profession, I wouldn't be surprised if puberty isn't starting earlier at all - we're just looking for it.