It was not as simple as being able to surround the city. The City of Stalingrad is located on the Volga River, a very large river that is critically important to logistics of the Soviet Union and the region. This river prevented the Wehrmacht from completely surrounding the city and let the Red Army to constantly resupply the defenders in the city with rail lines on the Eastern side and then with boats across the river. If the Germans simply surrounded the city, the Russians could just keep resupplying from the Eastern bank. If the Germans tried to cross the river nearby, they would leave the city at their flank which could allow the Russians to break out and attack their flank.

There is other considerations as well. Early on the German 6th Army had a distinct advantage, they pushed the Red Army almost completely out of the city. However, the Red Army was able to cling to some vital points in the city and was able to keep the Germans fighting there as they defended it. Additionally the 6th Army's logistics were already precarious as the battle began. The 6th Army was outstretched farther than the rest of the front as they had pushed to secure Stalingrad. This left their flanks exposed as it was a spear that struck at the city. It simply likely was not possible for the Germans during the time to do a complete siege of the city or mount any offensive on the Eastern Shore. This over stretching would have drastic consequences when the Russians used it against them during Operation Uranus where they struck the overstretched flanks and pinched the 6th army and encircled them in Stalingrad.

There also seems to be a recurring thought in the historical tradition to attribute some to the city's name itself. Hitler attached more importance to the city and conquering it than would be strategically necessary. Some attribute this more so than others. However it is a possible consideration. It also is on the opposite side as well, where the Red Army did pour more resources into the city than maybe necessary, however it led to the complete defeat of the 6th Army at the cost of many, many lives.

To summarize. Stalingrad was not really a city that could be sieged because of the geography, whereas the Russians had a secure hold on the eastern bank, logistically since the Germans were already overstretched with their spearhead to Stalingrad to begin with, and finally the moral implication for the Germans to conquer and lay waste to the city that bore the name of the Soviet Unions leader could have. The German's also underestimated the defense and resolve of the Red Army, and also underestimated that they could do a grand operation that was Operation Uranus.