The catch is that our secular calendar is an extension of the church calendar. While people argue whether or not they got 1 A.D. in the right place (let alone the debate over what date ought to count as Christmas) it is clear that a zero year was never intended and historians honor that convention. The year after 1 B.C. was 1 A.D.
Exactly...one of the biggest mathematical “breakthroughs” was when the zero quantity was accepted...or the “zeroth” power in formulations. I believe that began in the 1920s.
Try explaining to a class that the (second) millenium actually ended on Dec. 31, 2000 and the new one began one second after midnight of the next day. Or better yet, try explaining that to someone who paid $700 a night for a hotel for the “millenium” celebration in NYC on Dec 31, 1999, only to find out that they were a year too soon.