Why Man?

[The Squatter of Amon Rûdh]

Their rings certainly sped the process up, yes, but as I said above, they may not be the only cause.

Certainly Men weren't supposed to live for hugely extended periods, which the Rings allowed them to do by unnatural means. My inclination would be to look for the signs of spirit wearing out the bodies of longer-lived mortals, such as the men of Numenor, although the fact that their lives were naturally long may well invalidate the point.