Some parents or grandparents call their children lambs, or chickens – affectionate and loving terms. Many of us call our children kids.
Kid comes from a very old Norse word for a baby goat. The word has been borrowed and applied affectionately to small children for centuries, maybe because baby goats are so cute, like baby humans. It was being used as a common term of endearment for a child way back in the 1590s, when it was deemed slang.