It's all about when you start counting. Was the first year, "Year 0", or did it start at "Year 1"? What I mean is this: assume we are in B.C. Tomorrow would be 1 A.D., not 0 A.D. So it would take until 12/31 of next year for it to be the end of the first full year. So, it has to be at the end of 2000 for it be a new millennium.
Does that make any sense whatsoever?