Why did Hitler spend all of 1942 and shittonnes of men and resources autistically trying to capture and hold every inch of Stalingrad, and didn't even let them break out when encircled?
Is it really because if the "Le Stalin name" meme
>>3327747
No, it's because he had to defend his left flank. As the Soviets dug in in Stalingrad, they reinforced, so the Germans had to reinforce, so the soviets reinforced, etc.
As for why they didn't attempt a breakout, it's because it would be pointless. They were deeply encircled and the rest of the front was in disarray with that huge encirclement and the gaps of the Romanians, and the Germans needed to immediately prepare defenses, rather than be able to offer any support. By digging in and attempting a resupply, the troops could hope for a chance to coordinate their breakout. Attempting it unaided would have seen them destroyed much, much quicker.
At any rate, operation Saturn is right around the corner, and that fucks aby opportunity to coordinate, but also break out. There's no way the breakout is going to advance faster than the soviets.