When you want to know what a philosopher’s theory of normativity is, you must place yourself in the position of an agent on whom morality is making a difficult claim. You then ask the philosopher: must I really do this? Why must I do it? And his answer is his answer to the normative question. Christine Korsgaard, The Sources of Normativity, 1996. 18th parting, 2013.So, what is my answer to "the normative question?"
I can understand this form of the question if we viewed morality in terms of intrinsic values, divine commands, categorical imperatives, and similar moral entities. But they don't exist.
If we take this route, then we can be moral nihilists. We can say that moral normativity does not exist and throw morality in the dust bin.
But, seriously, think of society eliminating moral concepts - dropping all talk of justice, fairness, obligation, and permission. However, that does not imply that it has to be something that fits into Korsgaard's conception of "the normative question".
In fact, the virtuous person never faces a "tough moral question". The virtuous person does only what she wants. It's just that, being virtuous, what she wants and what morality demands are the same thing. Morality said, "Do what the good person would do - what the person with good desires and lacking bad desires - would do in this circumstance." For the person who already has good desires and lacks bad desires, this reduces to "do what I would do in this circumstance." There are no morally difficult questions.
Morally difficult questions arise for those of us who are not quite so virtuous and who realize our shortcomings. We recognize a gap between what we want to do and what a person with good desires and lacking bad desires would want to do. Then, the question can come up, "Why should I do what the person with good desires would do and not what I want to do?"
My next question is going to be, "Do you think you have a choice? You are going to do that which fulfills the most and strongest of your desires, given your beliefs. If you lack certain good desires and have certain bad desires, then you are not going to do what the person with good desires and lacking bad desires would do."
In other words, somewhere in there you have to have a desire - a desire to do the right thing, a desire to be a certain kind of person - to motivate your behavior or all of this questioning is for nothing.
A person with a desire to do the right thing has reason to anguish over the question, "Is this the right thing?" In the same way that a person who wants to win a game of chess has reason to anguish over the question, "Is this the best move?" The question, "Must I really do this?" if "this" is "the right thing" is "Yes, if you want to do the right thing." This is true in the same way that the answer to the question, "Must I really do this?" where "this" is the best move for winning a game of chess is, "Yes, if you want to win the game."
However, this is not a defense of subjectivism where "the right thing" is whatever one wants to do. "The right thing" is what a person with good desires and lacking bad desires would do. One of the implications of it being the case that this is "the right thing" is the fact that it us the thing that people generally have reason to praise, and its absence us something that people generally have reason to condemn. There is a right answer to what "the right thing" is and one's personal beliefs bear no necessary relation to what people generally have reason to praise or condemn.
Furthermore, morality is important. Promoting desires and aversions that tend to fulfill other desires has value for the sake of all of those other desires being fulfilled. There are reasons to insist that people generally adopt these attitudes regarding theft, lying, rape, kidnapping, and murder.
Yet, the truth and importance of morality - the urgency of getting people to adopt moral attitudes - is not necessarily compatible with Korsgaard's normative question. By the time the agent has reached the point where the normative question makes sense, with the agent is moral, or she is not. To the moral person, "Why must I make this sacrifice for the sake of my child," isn't a hard question. It isn't even a question.
If there is a question, it is, "Why make people so that they act this way?" The answer to that is, "For the sake of those desires that such people tend to fulfill or, at least, prevent thwarting."