The reason is that year 0 never existed. The year 1 BCE was followed by the year 1 CE.
Culturally, anthropologically, and psychologically it might be a different matter. But 2000 years had not passed before the end of that year.
The calendar was back-dated 500 or so years after Jesus, by a European guy before Europe had the concept of zero, leaving us with 1-indexed years. Then, 200 or so years after that, another guy (still lacking the concept of zero) made the even less venerable decision that the year right before 1 AD would be 1 BC.
We could just decide today that 0 came right before 1 AD and was the first year of the first century AD. Then we’d just have to shift all BC dates by 1 year in all our history books.
The upside would be that arithmetic on year labels starts working again. The downside is that there are way too many history books and no one will ever do this.
Of course, the easier way out is to just decide today that either 1) the first century began in 1 BC or 2) the first century had 1 fewer year than all the other centuries.