Drop the Baby

When someone has a baby, and another person asks, “What did you have?”, why does the mother (or father) say, “We had a baby boy [or girl]!”?
Why do they have to include the word “baby”? Is it necessary? What … do some wacky women give birth to adults? Isn’t it enough to just say, “We had a boy” or “We had a girl”?
Drop the “baby”, I say. (Only figuratively, of course!)