By the time the German counterattack to relieve the Stalingrad pocket was launched, it was way too late. The Soviets were constricting the pocket like an anaconda and the weather was far too miserable for such an attack to succeed. Moreover, the Soviets were now threatening to cutoff German divisions still in the Caucuses further south of Stalingrad, so FM von Manstein had to focus his efforts on getting them out and preventing yet another German army from being trapped and encircled. The only chance the Sixth Army trapped inside the Stalingrad pocket was in the first or second week of the encirclement, when it had the strength to break out. But Hitler stubbornly refused any breakout attempt over-ruling the finest military minds (and common sense) thus condemning an entire army to a very grisly fate.
Paulus should have disobeyed Hitler and fought his way out when he could. Of course, he would have been fired or possibly arrested, but a lot more of his men would have lived to see Germany again.