Pronoun "it" for baby?

Does anyone know why the word "baby" is referred to by the pronoun "it" rather than a human pronoun. Is there an historical/etymological reason?

I have always assumed that this is because small children are unidentifiable except to the doting parents. If you take a wild guess and call the child "he", there is a 50% chance that they will be offended that you can't tell their beautiful daughter from a boy; "It" will draw a correction, but not offend them. (I have noticed a similar effect with dogs and dogowners.)
This assumes you are not referring to unborn children, who are properly called 'it' because not even the parents can tell without medical assistance.

It is already the case in Old English. The gender is neuter and the pronoun is "hit". The word cild (child) is neuter and so is bearn another synonym for child (Scottish bairn). Baby itself is a later addition of Middle English.

In Modern German, which shares a common ancestry with English, all diminutives (-chen, -lein) are neuter regardless of the original gender.

• Die Maid (maiden) => Das Mädchen (girl),
• Der Mann (man) => Das Männlein (manling).

There might be other similar cases in other Indo European languages but the Latin puer is masculine and the Greek παῖς is either masculine (boy) or feminine (girl).