Consider WHY differing ideologies would matter to each superpower?

Why couldn't these two superpowers simply co-exists?

What reason/motivations would each nation have for opposing so intently the other ideology (enough to divide the world)?

What MORAL/ECONOMIC/POLITICAL reasons/motivations might each side have had for opposing the ideology of the other so intently (enough to divide the world)? Worded differently, why would the US care if the USSR and other nations chose to practice communist ideals? (and vice versa)?