<rant> I'm annoyed by this argument, which came up again at the start of this year in dumb Twitter discussions about whether 2020 marks the beginning of a new decade.
2000 was not the final year of the Nineties. 2000 was the final year of the second millennium, and of the 20th century, and of the tenth decade of the 20th century. The Nineties were the years 1990-1999, the tenth decade of the 20th century were the years 1991-2000. These are different ranges, but we also use different terms to refer to them. There is no logical problem. There is only a problem with the assumption that these different terms "should" refer to the same concept.
So did 2020 mark the beginning of a new decade? Yes, it marked the beginning of the decade we might call the Twenty-Twenties. It did not mark the beginning of the third decade of the 21st century; that will be 2021. </rant>