Because the Russian army was for greater than the German's, and with the Japanese getting whupped by the Americans they had no other allies.
While bogged down in Russia, declaring war on the US would soon create a two front war. As history shows, big mistake.
Declaring the War of 1812 with Britain
Russia declaring war on Germany to protect its ally Serbia.
Russia declaring war on Germany to protect its ally Serbia
Russia declaring war on Germany to protect its ally Serbia
Declaring war on the USA after Japan declared war on America. Germany declared war on America hoping Japan would declare war on Russia. Since Japan did not declare war on Russia (Russia would later declare war on Japan), Germany did not have to declare on America. If Germany had not declared war on the USA, America would have difficulty in declaring war on Germany (although USA and Germany naval vessels in the North Atlantic were shooting at one another in 1941). If Germany had not declared war on the USA, then Hitler would not have had to face the military men and equipment of America. Although Russia fought the majority of land battles against Germany, it was American men and equipment that helped Russia and Britain and other Allied nations to defeat Germany.
Russia began moving it's army toward the russian-Austrian border. it mobilized Russia along the German border
When Russia found out that Austria-Hungary was declaring war on Serbia, they came into alliance with Serbia for several reasons.
Technically, Serbia. However WWI is widely referred to by Historians as 'The War Nobody Won'. Austria declaring war on Serbia, the Serbs’ allies Russia declaring war on Austria, the Austrians’ allies Germany declaring war on Russia and the Russian’s allies France and Britain declaring war on Germany. America eventually entered on the side of Serbia et al due to a few incidents with German U-boats and Germany surrendered. If you work backwards operating under the system of official declarations via the various alliances the winner is Serbia (whose country was mostly pounded into gravel in the process) and their allies: Russia, France, and Great Britain.
....Russia and France were partners in an offensive/defensive treaty they had concluded earlier. So declaring war on Russia according to the Treaty 'automatically' meant that a state of war came to exist between Germany and France.
1. Declaring war on the US after Pearl Harbor. 2. Invading Russia.
The Axis was composed of Germany, Italy, and Japan. FDR could not legally enter the war until the enemy country declared war on us. When Japan attacked Pearl Harbor, that was clearly a declaration of war by action, so FDR responded by declaring war on Japan verbally. Hitler then made the mistake of declaring war on the US verbally, so FDR responded by declaring war on Germany verbally. Mussolini also made the same mistake as Hitler, with the same result on Italy. Had Hitler and/or Mussolini not declared war on the US first, FDR could not have declared war on them and we could not have fought them.