Technically the Germans didn't need to occupy Stalingrad, as per the original operational directives.

The overall operation of Case Blue was to drive south and seize the Caucasus oilfields at Maikop and Baku. However, the German northern flank needed to be protected. For this reason Army Group South was split in to two groups. Army Group A, and Army Group B. Army Group A was tasked with driving south to capture the oilfields, while Army Group B was tasked with securing the Northern Flank along the Don and the Volga, which included Stalingrad.

While the Army Group A made their push down into the Caucasus's, Army Group B kept on pushing eastwards. However, the newly established Stalingrad front was putting up fierce resistance. It was around this time in July that Hitler Rewrote the operational directive from just the destruction of key industrial facilities in the area around Stalingrad, and blocking and disruption of commerce on the Volga, to the capture, occupation, and destruction of the city itself. It more or less became a personal obsession of Hitlers, being that the city bore the name of the Soviet Leader - and the capture and destruction of the city would not only deliver a huge propaganda victory, but would also firmly secure the German Northern Flank.

However, as we can see, the fighting in and around the city arguably became something much larger than the entire Operation itself. So much was attached to the city by both sides. On the one hand, the German's saw it as their ticket to victory in the south. Once they destroyed the city and pushed the Soviets over the Volga, nothing could stop them. For the Soviets, it was their last stand. They could not lose the city which bore the name of their leader, and a defeat there was not a option, if they were pushed back over the Volga, it was over.

This is why the battle became one of the most decisive, if not the most decisive of the war. So much was at stake, the effort of millions and the inevitable meat-grinder it became.