Shelly Kagan on Deriving a Moral System
If something like this picture is correct, then defending (or attacking) a normative theory will virtually never be an open and shut matter. Almost any normative theory is likely to have its counterintuitive aspects, and people can sincerely disagree as to which theory is, on balance, the most attractive. That is why there are few or no "knockdown" arguments in ethics (or anywhere, for that matter). All you can do is point out the attractive features of your own favored theory, explain why you are prepared to live with its various unattractive features, and try to show that the alternatives are even worse.
What this means is that you will not be able to persuade eveyone of the truth of your position. So be it: you cannot persuade everyone. But that does not relieve you of the obigation to try to defend your moral views, and to revise them if you cannot. For each of us must decide how to live, and given the importance of that decision, it behooves us to examine whether our own moral views can indeed be defended.