Why would an element like chlorine prefer to exist as a diatomic molecule instead of as an atom?

All the chemical elements of the universe tend to join with others to achieve the maximum possible stability.

Chlorine is an element of very high electronegativity (3.16), which means that in its atomical from is very likely to form molecular bonds with other atoms such as oxygen, nitrogen, carbon and itself. In doing so, chlorine wastes its energy to create these links, and as a result, loses some of its reactivity.

Once in this molecular state, it can only react when the activation conditions are sufficient to reach a higher level of stability.