
But a person starts out at age 0, the calendar didn't; the appropriate comparison would be saying someone is 1 at the moment of birth. The third millennium, the 21st century, and the first decade of the 21st century, all started 1 January 2001, not 2000.

The first year wasn't "0". It was 1. Ten FULL years must pass so therefore 31st Dec 2010 is the last day of the first decade of the 2000's. January 1 2011 is therefore the first day of the next 10 years, ending on 31st Dec 2020.

A lot of posters have made this argument here; I don’t think that holds water. The first year wasn’t 0 or 1 or 2 or 3 or anything like that. We did not adopt the current calendar from year 0 or year 1, 2, 3 etc. we adopted it much later. The Gregorian calendar was introduced by Pope Gregory in a decree in 1582. So the first year was really 1582.
So how do we know that the calendar didn't start at year 0? We don’t. The reason average person thinks that it is the start of the new decade is simple. The second digit changes. Going form 2009 to 2010, the second digit changes from 0 to 1. Simple, and end of story.
Indeed, that is why 1 Jan 2000 heralded the new millennium, nobody paid much attention to 1 Jan 2001.
Sometimes common wisdom goes against scientific wisdom, and this is one such instance. And since it is not a significant matter, it is an unimportant subject; common wisdom prevails here, and tomorrow is indeed regarded as the start of the new decade.

I'm inclined to propose the opposite argument. When we count we go from one to ten (0), in all other instances, so why change it for the date? What the years were called 2000 years ago is irrelevent (if you want to correct for that, then the current year probably isn't "2009"). I think the second decade starts Jan.1 2011.