I agree with the author. The year 1 A.D. ended one year after the birth of Christ. The year 10 A.D. was the last year of the first decade of the western Christian calendar. It's very simple math, but seems to escape many.
Well - the author is wrong. We don't count decades as we do centuries - we count them as ordinals - i.e., the 20's, the 60's, etc. The first day of the '20's' was Jan 1 1920 - the last day of the 20's December 31, 1929 - followed then by the first day of the 30's, etc.
Just for fun, listen to Dr. Walter Williams on the topic.
Centuries certainly run 100 years, counting the first century is 1-100, the second century is 101-200, etc.
We tend to refer to decades as the fifties, the sixties, the seventies, etc. The decade of ‘the fifties’ is the ten year period of 1950-1959. The sixties is 1960-1969. I don’t think people consider 1970 as the final year of ‘the sixties,’ but rather the first year of the decade known as ‘the seventies.’