If we could all agree that the years 1-99 were the zeroth century, it would make things a lot easier. amirite?

Nah it was the 1st,

It was the first one hundred years, thus, at year 100 the first century was completed.

That's why it's called the first century. Because it was.

But it wasn't, so we can't.

We would also have to agree that the years 1-99 BC were also the zeroth century BC, if we wanted to avoid the same problem with BC centuries.