If they attribute precocious puberty to animal growth hormones, will eating those foods make my breasts larger?

No. Precocious puberty is not from animal growth hormones and no eating the meat of animals fed growth hormones won't change your breast size.
No. Human growth hormone (or mammalian or synthetic gh) is a small to medium sized polypeptide that will be broken down in your digestive tract into basic building blocks (amino acids) and absorbed into the blood stream. When gh is given to people or animals, it must be injected. Even when gh is injected into people, breast growth is not a usual result of it's use.