Is there a reason to avoid the Nikon 80-200 f/2.8 on a Nikon D7000?

I just got my Nikon D7000 and I was not satisfied with the kit lens that came with it (18-105mm VR), so I have now set my eyes on an 80-200mm available for $1000 on a local store.

However, I have heard photography sites that say never to pair up the 80-200mm f/2.8 with a DX camera an instead to go for the 70-200mm f/2.8 VR2, which is more than twice the price of the 80-200.

For budget reasons, I am not able to go 70-200mm, but I would not want to waste money on an 80-200 if it will not work as I expect it.

I do mainly sports photography and candid shots of people from events, so I need the zoom and the f/2.8. I also plan to do small music videos, so I need the zoom and the f/2.8 aperture, again.

So why, exactly, do some people say not to pair up the f/2.8 80-200mm with DX cameras? Or in general, why would I not want to pair up a lens designed for FX cams with DX cams?