What exactly is being asserted by those who claim (and denied by those who deny) that there are agent-relative reasons?

I motivate the idea of an agent-relative reason in the following way. I have a personal project, which is to write a good book on ethics. This is very important to me; it informs and gives sense to a central decade of my life. But I know that in some sense it does not matter much whether I succeed or fail. The world will not be much the richer for my success, nor much the poorer for my failure. It is hard to express this point uncontentiously, but there is enormous pressure to say something like “it doesn't really matter” or “it doesn't objectively matter” whether I succeed or fail. But it matters very much to me. We might try to say there is great value for me if I succeed, but it is not really important whether I succeed or not. Now the point here is that I know both these things. I know that it matters to me very much and that it doesn't really matter as much as it matters to me. Neither of these things is hidden from me. I have a perfectly clear idea of how much it really matters, and another perfectly clear idea of how much it matters to me. Neither idea is a distortion of the other.