Question

at their meeting of January 1942 what argument persuaded Roosevelt and prime minister Churchill to pursue Europe first strategy

Answer 1

Germany was threatening Great Britain and the Soviet Union -- Germany was the greater immediate threat to them.

Germany was the primary threat to Great Britain, so Churchill did not really need persuading about that. It was also feared that Germany was the greater threat to the Soviet Union. President Roosevelt was under pressure in the United States to focus on Japan because of Japan's attack on Pearl Harbor, but Germany's declaration of war against the USA (on Dec. 11, four days after the Pearl Harbor attack) made the Europe First strategy agreeable for the USA. The Europe First policy was decided at the Arcadia Conference held in Washington, DC, Dec. 22, 1941 to Jan. 14, 1942.

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Answer 2

Churchill believed that it would be better to first take Sicily then Italy saying the communication lines are not good and it would not be easily to pull them out in an event of an invasion of Northern Europe. He added that at that point Germany would be weakened since it also fighting in the east against the Russians. Roosevelt agreed to this strategy but emphasized more commitment to the Pacific where Churchill agreed to send troops to Asia.