There are many aspects of modern life that increase global competition. Perhaps the most important is our materialism. The fact that we all want so many material goods helps to create competition and conflict in the world.
Because we are so materialistic, we demand plenty of material goods at the lowest possible prices. This leads to a situation in which we face economic competition from all over the world. This happens since we want cheap goods and people in other countries can supply them at lower prices than American workers.
Because there is so much economic competition, we also get conflict. We have, for example, conflict with China as its economy catches up to ours (at least in gross size). Many Americans fear the rise of China and therefore put pressure on our government to resist it. This helps to lead to conflict (not yet military, but conflict nonetheless) with China.