Another way to put it is that we don't number calendar years the way we do birthdays/ages.¹ Which probably accounts for some of the popular confusion here.

Your 23rd birthday is at the end of your 23rd year, and you're "23" from then until the 24th birthday. But you're actually progressing through your 24th year at that point.

Conversely, during the year called "2000" we were in the 2000th year. We completed 2000 years at the end of it. Upon which we started marking progress in the 2001st year.

---

¹Gregorian calendar/Western-style birthdays

This makes sense. That being said, convention is very useful until it is broken for further optimization and setting better standards. I'm just not sure that a debate over "when it really started" is useful in that specific applications can define the start and end based upon what is needed rather than what is right, wrong, or accepted by convention. One exception to this is that non-specialists or students may learn something from the debate (provided it is public). A more useful debate would be whether or not we should rid ourselves of daylight savings time!