First it's a catastrophic rout, then it's a tactic?
I think that some clarification is needed here.
D Inqu was talking not just about the pullback of AG South forces to Kharkov, but also the withdrawal / rout of the German Caucasus Armies - which was a pretty utter catastrophe.
The issue is that the Germans sent substantial forces - including an entire Panzer Army - further south of Rostov into the Caucasus, in a vain attempt to capture Soviet oil sources. While doing so, they left their flanks exposed to Soviet forces in Stalingrad; which explains why 6th Army and 4th Panzer Army was fighting at Stalingrad in the first place. Even worse, due to the massive extension of the frontline, you basically had a gaggle of Axis Minor Armies - Romanians, Hungarians, and Italians still waiting for equipment the Germans promised them - shoring up all the holes in the line in this battle area, and all of these units were badly overstretched themselves.
It was basically 1940 all over again, except the Germans were doing all the mistakes the French did.
Manstein's "achievement" was that he managed to pull a portion of the Caucasus armies out after the Soviets surrounded Stalingrad and threatened to retake Rostov - which was the Caucasus' armies sole supply line. He succeeded in getting First Panzer Army out, but the rest of the forces - including a lot of Axis minios and locally raised units that the Germans typically don't count among their losses - were essentially wiped out along with the Stalingrad pocket. This is the rout that D Inqu is talking about - Manstein's "withdrawal" actually left behind a lot of units, and his memoirs and pro-German post war propaganda made a big deal of the fact that he "saved" 1st Panzer Army while leaving the rest of the Caucasus forces to rot (and really, this trope of Germans "fighting out" of Soviet encirclements when in reality only bits and pieces managed to evade capture and the rest of the casualties were simply covered up or not counted repeats over and over again especially by 1944).
That said, I do think he's a bit harsh on Manstein. Manstein saw an opportunity - the Soviets overstretched themselves by trying to reach the Dnepier instead of just limiting the offensive to the Don - and he made them pay for it with pretty good results (more reliable sources would say that he destroyed a Soviet Tank Army and some 50,000 Soviet troops).
But it doesn't change the fact that it wasn't necessarily a brand-new tactic that would save NATO from Soviet tank hordes (that's just the Cold War version talking), and people keep forgetting the Germans had to commit a freshly refitted SS Panzer Corps for the counter-offensive and it got badly mauled to the point that the SS had to start resorting to stealing recruits from the Luftwaffe and Wermacht after Third Kharkov because they had exhausted their own ideologically-approved recruiting pool.
Third Kharkov was a German tactical victory born out of a Soviet mistake and an alert German commander who took advantage of their mistake. But t is not a modern Cannae that the Cold War fanfiction writers made out to be. If we tried to do it Manstein-style in a hypothetical Third World War, it would be like the Bundeswehr claiming victory after destroying a Soviet Tank Army (let's say 3rd Shock), but in doing so left all the Belgian, Dutch, and Danish units to die (they're not good units anyway!) while suffering heavy losses themselves. It's not going to alter the strategic balance in the long run and is just another road down a slow rot.
