If something is morally good, then everybody has a moral reason to prefer it, isn't it? But if Lucretia has a moral duty to do something, then, philosophers say, Lucretia -- and not necessarily anybody else -- has a moral reason to do it. Does that make sense: if it is a moral duty, it should give moral reasons to everybody, shouldn't it?
Suppose we accept your
Suppose we accept your proposal that if something is morally good, then everybody has a moral reason to prefer it. It doesn't follow though, at least without additional argument, that if everyone has moral reason to prefer something, everyone has a moral duty to do that thing. For there may be moral reasons incumbent only on some rather than on others. If Lucretia has a child, I may concede both that her child's being well fed is morally good and that everyone has a moral reason to prefer her child being well-fed, but it may not be true that everyone (me included!) has a moral duty to feed her child. For instance, it may be true that I don't have such a duty precisely because Lucretia does have such a duty — she being her child's mother, she has a special duty to ensure that she is well fed that I (and others) have. Such special duties seem relatively common: A firefighter has a duty to rescue someone that I do not. I have a duty to educate my students that the firefighter does not. And so on....
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