Argument #1
The Court should rule in favor of Korematsu. This "is the case of convicting a citizen as a punishment for not submitting to imprisonment in a concentration camp, based on his ancestry, and solely because of his ancestry, without evidence or inquiry concerning his loyalty and good disposition towards the United States." 

Argument #2
The Supreme Court should rule in favor of the government. "It should be noted, to begin with, that all legal restrictions which curtail the civil rights of a single racial group are immediately suspect. That is not to say that all such restrictions are unconstitutional. It is to say that courts must subject them to the most rigid scrutiny. Pressing public necessity may sometimes justify the existence of such restrictions."