What does polar opposite mean?
For example, The polar opposite to capitalism, communism, was also a big issue during the time in which Vonnegut was writing his short story – the Cold War was in full swing in the early 1960’s, with the Bay of Pigs fiasco and the Cuban Missile Crisis – but, once again, Vonnegut seems to avoid this issue explicitly in this short story.

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Think of magnets, they have positive and negative poles - they repel each other.  Polar opposites are two things that tend to repel each other or are mutually exclusive

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When you talk about the polar opposite of something, you referred to the absolutly opposite word of that. Like south pole is the opposite of the south pole.
Capitalism vs Comunism 
a tidy person vs untidy person
handsome vs ugly

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polar opposite= that which is conspicuously different in  the most important respects.