You have repeatedly talked about the land and men advantage Russia had, so even if the Germans captured Moscow, the Red army could continue the fight anyway until the British and Americans came to their aid.
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Psychology. The Nazis believed that the capture of Moscow would lead to Stalin either surrendering or being deposed by Zhukov.
Moscow had strategic value as well as psychological one.
Moscow was a central transportation hub of Soviet Union, particularly for railway. If Moscow was to be taken, Southern, Northern and Eastern parts of a Soviet Union would be effectively cut-off from each other - there are other roads and railways, but their capacity would not be sufficient to sustain coherent war effort. Moscow was also a major industrial center, even with a significant number of factories being evacuated to Urals.
Of course, that doesn’t mean that Germans would automatically win the war if they were to take Moscow, but it would give them a significant military advantage.
Is there an argument that since they are part of Army Group Center they are just looking for ways to justify why their sector is the most important?
It’s very likely. The commanders of the other army groups used similar arguments to justify why their sectors were most important. The symbolic and cultural importance of Leningrad to the Bolsheviks was used to justify prioritizing Army Group North, while the wheat fields of Ukraine and oil fields of the Caucasus were used to justify prioritizing Army Group South.
the simple answer is Moscow is the capital. Its more of a symbolic victory than anything and in the case of Poland and France once the capital was taken the countries capitulated pretty fast, The Soviet union however was a far different beast than poland and france, arguably if Moscow was taken it would not have ended the war and likely would have caused resistance to get even worse as Moscow would have quite likely become a martyr