> They know the day doesn't begin at 1am, they know babies aren't born 1 years old. This isn't a computer-specific concept in any way.

This is true, and an interesting point, but also nobody describes a baby as being zero years old, or the time as being zero-o'clock. People avoid zero in these situations and find alternatives - i.e. 3-months or 12.30am.

Personally I see both sides but the point is that whenever you make something divisible, the first unit is 1 and that's what people call it.