It's certainly not what I'd call an optimal choice for the campaign, but with the majority of Russia's southern armies surrounded and destroyed at Kiev, what did the Russians have to stop them? Particularly given the likelihood of Stalin still perceiving there to be a threat to Moscow (witness the response to Germany's "case blue" operation of 1942.) Hitler's already thrown away probably the best chance at Moscow. Now he's moved half of AGC's Panzers so far south why not gamble? Particularly as I doubt the Russian army was operationally skilled enough to successfully break through the German flank and cut off the Caucasus spearheads.
Actually, I've never been convinced that Hitler's move south was such an enormous mistake. The Wehrmacht's eventual success in any Russian campaign was predicated on the destruction of the enemies main armies in the field. Whether the southern armies were high quality or not, they still represented a large percentage of the Soviet Union's mobilised strength, and they had had some success at holding up Rundstedt's drive south of the Pripet Marshes.
Actually, I've never been convinced that Hitler's move south was such an enormous mistake. The Wehrmacht's eventual success in any Russian campaign was predicated on the destruction of the enemies main armies in the field. Whether the southern armies were high quality or not, they still represented a large percentage of the Soviet Union's mobilised strength, and they had had some success at holding up Rundstedt's drive south of the Pripet Marshes.