Popular culture, which is generally content to be ignorant.
2000 is the end of the old millennium, not the start of the new one. The 20th century started at ~12:00:01 AM on January 1, 1901, and ended at ~11:59:59 PM on December 31, 2000. By that reasoning you were born in the 200th decade, indeed making you a 90's baby in that sense.
If the ancient Christian year-counters had used a year Zero – and a day, hour, minute, etc Zero, too – in their Christian calendar, then we wouldn't have this issue.
But popular culture, which doesn't require knowing any of the foregoing, just cares about the digit in the tens' place, and so doesn't account you as being a 90s baby.