The Army of the Tennessee wasn't going anywhere, it could either go after Sherman or batter itself to destruction against the Federals in Tennessee, Hood chose the latter.
By that stage in the war it was so over-matched Sherman didn't have to go against it.
"...if the gentlemen of Virginia shall send us a dozen of their sons, we would take great care in their education, instruct them in all we know, and make men of them." Canasatego 1744
