The problem with your logic is that you cannot tell me what happened in year 0.
In fact, it would be hard press to try convice someone that 1960 had any relations, socially, to 1969.
The problem with your logic is that you think that year zero matters in everyday language. It doesn't. If a child is born on July 17, 1970, I don't think anyone would say the child was born in the sixties. Do you? I will agree that he was born in the 196th decade AD, but that's an odd construct and not one conducive to communication.