There was no year zero AD. December 31, 1 BC would have been followed by January 1, 1 AD. January 1, 2 AD marks the one year point since flipping over to AD. Counting forward from then, 100 years have passed as of January 1, 101 AD.
Thus, it takes until January 1, 2001 for 2000 years to have passed since the first day of AD, January 1, 1 AD.