The question is, of course, a challenge to justify one’s adherence to morality. One must show that well informed rational beings would choose to behave morally.  One can think of two types of justification: internal (validation) and external (vindication).
    An internal justification is from within ethics itself: we have a good moral reason to be moral, and that's all that is  required. The problem here is that what's asked for is external justification.  That is, one is asking:  why should the moral way of life have priority over other conflicting ways of life (religious, self interested etc.)?  Why shouldn't I use Gyges' ring immorally?
    An external justification addresses a global issue:  why should I be moral at all?  Brief reflection shows that this can be an impossible question to answer if it requires to show that morality should have priority even from the standpoint of another, and opposed, way of life.  For example, if self-interest and morality do come into conflict, it would be unreasonable to demand that the defender of morality show that from the standpoint of self-interest we should be moral.  Or, if religion and morality conflict (think of Abraham on mount Moriah), it would be absurd to require a religious justification for why one ought to choose morality rather than religion.  Of course, one might believe that morality and self-interest never come into conflict.  For example, Paley thought that since God exists, wants us to be moral, and will punish and reward accordingly in the next (eternal!) life without fail, real self-interest and morality never diverge.  Or, one might say that immoral behavior harms us in the sense the harmony of our mental life is jeopardized: doing wrong may provide some advantage but thwarts our nature preventing us to be the sort of being we could be.  Or, one might argue, as Foot did, that behaving immorally while pretending to be moral (the obvious case in which immorality seems advantageous) is ultimately psychologically too demanding and ultimately leads to unhappiness.  An analogous point can be made with respect to religion: one might believe, like Clarke, that morality and religion never conflict, and that when they seem to disagree one only has to look more carefully to find agreement.  All of these views see to me wishful thinking: Allen's Judah claims to have overcome his psychological problems and to be happy, even if occasionally he has a "bad" day in which he is troubled by his conscience (but is it his conscience as the receptacle of his rationally, at least for him, accepted values, or his conscience as the psychological result of his religious upbringing?).
Some philosophers, e.g., Kant or Frankena, have argued that rationality itself demands morality, but their arguments, such as they are, have been the subject of much justifiable criticism.
    One might reject the idea that one can provide a justification for morality, and argue instead that a moral way of life can stem only from an existential commitment, from a choice of life.  In this respect, then, morality would be similar to religious faith: one must accept it or reject it but at the same time abandon hope for any higher level of justification.  But then, the same courtesy would have to be extended to immorality.