I've never done anything because I believed it to be right

It's true! I have, on the other hand, done things because they were right. My belief aims to capture this fact, but doesn't thereby become my reason for doing the action.

This looks very odd, but it's relatively easy to show. If my reason for doing P was that I believed that P were right, then I should say of hypothetical contexts, where I no longer have the belief, that I no longer have the reason. But this just isn't true of most reason we take ourselves to have. If I imagine myself without the belief that being kind is good, it's just not true that I imagine myself in a situation with no reason to be kind. Reasons aren't dependent on beliefs in this way.

(In some cases, your reasons for actions do come from your beliefs. If I believe that everyone is out to get me, then this is a reason to get help. This satisfies the condition above: in hypothetical contexts where I lose this belief, I no longer have the reason to get help. But this kind of reasoning is obviously not the standard kind.)

Does this matter? Well, there are two upshots. First, it's not clear how theories of "motivation" come out after we think about things in these terms. People aren't motivated by combinations of beliefs and desires, as some (not all!) Humeans would have it. Second, I wonder if this is sometimes in the background for supporters of naive relativism. If people's reasons depended on their beliefs in this manner, then things are pretty relative to the agents opinions! Still, if this is false, then relativism loses this potential ground for support.

Probably more on both of these in the future.