Why should someone choose to be good?

Because people who are not good are punished, formally or informally. A society that does not punish bad people perishes, so societies develop ways to make people behave well. Religion is one such means, but a respected elder is another. My dad told me that an honorable man keeps his word. That was enough for me. Religion is a useful tool for some, but it is hardly necessary, and its utility says nothing about the truth of its theology.