Symbolism.
Conquering a city named after Stalin would have been a huge morale booster for the Germans, and a huge blow for the Soviets.
So it had to be conquered/defended at all costs. At a horrendous cost.
When Von Palus and the 6th army were encircled. Failed to break out then surrendered against the orders of adolf Hitler. Marked the beginning of the end for the Germans on their Eastern front.