Why do cities exist?

Because it would make better armies and would help with trading

2nd answer:

True, but people originally got together as protection against animals and other human colonies. They found that a big shelter like a cave was handy, as not every individual could find his own cave. Later, people began to build huts in social groups, for protection and because they had found out that gathering nuts and berries was more efficient with many women at work doing it, and because it took a number of men getting together to track and bring down animals to eat.

Later, these social groups started building fences or walls around their encampments so that they could be safe from animals at night when they were asleep. These were the first villages. Villages naturally led to larger social groupings, and eventually to large groups later called cities.