Which shows that you weren't born in Japan: people there are born 1 year old.

They are not even though they start counting from 1. The child is still zero years old.

It's a matter of (natural language) terminology. It's the difference between asking "which year of your life are you currently in" as opposed to "how many full years have elapsed since you were born?"

Agreed. My previous reply just pointed out that 1 is not "how many full years have elapsed since you were born?". The answer to this question is still 0.