Why would a 3 year old child have armpit odor?

Armpit odor comes from the action of bacteria on the skin which digest some of the components of sweat, and in the process create chemicals with the smell we know as "body odor." However, the sweat that causes is this is not from "regular" sweat glands that are located all over the body, but rather from special sweat glands called apocrine sweat glands located in the armits and genital region. Typically these glands become active at puberty - thus, early development of body odor could be consistent with a hormone imbalance or the early onset of puberty - this is by no means certain, but you should have the child checked out by a pediatric dermatologist or a pediatric endocrinologist. There would be more reason for concern about a hormone issue/early puberty if other secondary sexual characteristics are also appearing (notably, pubic and/or underarm hair, breast development in a girl, facial hair in a boy). I don't at all want to panic you, but if the problem has been persistent then it is well worth pursuing.

Answer #2Could be soy milk. The isoflavones imitate hormones. I do NOT recommend soy milk for prepubecent boys. Below is a link to an article.

http://www.mothering.com/discussions/archive/index.php/t-12530.HTML

I would leave off soy products and wait 2-3 weeks and see if it improves.