http://www.projectpluto.com/no_zero.htm
Frankly, this isn't the logic I use to defend it (I say it's 2000 because that's what everyone calls it, and if they wanted the new millennium to start a year later, they should have called it 1999), but if you're going from a historical perspective, there's still good reason to consider 1 BC to be 0 AD (and vice versa if you wish).
I graduated high school in 2001, so at the time I liked to think of 2001 being the real first year of the millennium because it meant that we were the first graduating class that millennium. :) Yeah. And there is no year zero, so it IS technically true as well... kind of. I mean, thinking about it right now, we don't re-adjust when decades or centuries start, we just said 'the first one starts from 1', so it probably makes more sense to say that the first 'millennium' was 999 years long. But you could go either way on it.
Anyway, as for the link, that's an interesting argument in that link about 1 BC being the 'real year zero'... I don't know if I entirely buy it though, since they didn't have a 'zero' so I'd think that if he meant for what later was called 1 BC to be 1 AD he'd have called that year 1...
In other news, so far 2016 feels pretty similar to 2015. :p
You don't need to think of it as a 999 year long millennium. You can still think of it as 1000 years long. Just adjust accordingly, or not at all really. It's always been rather petty semantics anyway.
But if it's only 999 years long how can you think of it as 1000 years?