Rob Redmond posted an interesting article encouraging the martial arts instructor not to advise students on when to use their skills. While morality is an area fraught with difficulty, it's an abdication of responsibility to say that the instructor should avoid the topic altogether. As with most things, there is a question of balance.
Karate practitioners are not necessarily experts on stretching, or fitness, but karate instruction will typically involve some coverage of those topics because they have bearing on the practice. A wise instructor will not claim to have all the answers. He or she will be able to say "I don't know", and research the answer, or recommend a source where the student may find the answer for him or herself. A wise practitioner striving to better himself will do some research in all areas that have a direct bearing on his practice.
A critical skill in any field of study is skepticism, especially on received wisdom. There's a time and place for questioning, but there should be some space for analysing any tenet of a field.
With those preliminaries covered, what should the martial artist study with respect to morality? My initial reference for all students and teachers is Forest Morgan's book Living the Martial Way. It is extremely direct, accessible and not dogmatic. Although it lacks the scholarly rigor of the philosophical writings of, for example, John Rawls, it is much easier to read, and a better use of time for more martial artists than deeper philosophical treatises.
All martial arts teachers are teaching morality whether they think they are or not. Simply how one conducts class and carries himself in training is teaching morality. Some teachers bully their students. If a student asks a respectful question at an appropriate time and the teacher dismisses or ridicules the student, that is teaching morality. If elder students cause injury to their juniors on a regular basis, that is teaching morality. The formalities typical in traditional Japanese martial arts teach a certain moral code of respect for authority. When teachers are gentle and encouraging with their students, they are teaching morality. It is simply not possible to divorce the physical practice from the morality inherent in how human interactions are guided in class, whether by example or explicit direction.
In Funakoshi's autobiography Karate-do: My Way of Life, he teaches many moral lessons. While obviously a gifted and tireless physical practioner, his life and stories provide strong moral lessons of perseverence, respect for others, non-violence and personal dignity. The strength of his character may be as much the reason for the spread of karate as the physical practice itself.
Aikido is an art that embodies a certain non-violent code. There is no attack in this style. There are practitioners of the style no doubt who have internalized the martial skill without the moral lesson, but perhaps fewer than in other arts. The physical practice should teach a moral code. The attacker is not directly subdued. His own energy is used to bring him to a place that is safe for him as well as the defender. The defender does not run and is not vulnerable, but does not himself attack. Karate similarly has the oral tradition of having no first attack. While one might question the application of the first move in each kata, the simple presence of that oral tradition is teaching a useful moral lesson.
Moral and emotional lessons from the martial arts are far more important today than the physical practice. If a school simply gives the sociopath better combat skills it's clearly doing something wrong. Most of us will thankfully never be in a combat situation. So, what is the value of karate? It's nice to be fit, but I hope there's more to it than that.
Martial arts is a laboratory for self-improvement. It is where we can "seek perfection of character" as Funakoshi states in the dojo kun. Confronted with a much more senior practitioner in sparring, the junior student learns how to face adversity in a most personal way. He can learn how to strive against a situation which is likely unwinnable. He learns how to lose with grace and profit from the experience. He learns how to confront his own fears and demons.
A practitioner sparring with a more junior one hopefully learns self control, grace and compassion. He can learn how to teach, not just how to conquer. He wins with modesty. He learns empathy, striving to challenge the junior just up to the point the student can take, but not beyond.
In sparring an equal, or near-equal, or in solo forms we can all strive to focus on ourselves. It is natural to compare oneself to others. If we compare ourselves to our seniors to find examples for improving our practice, that may be good. If we look at others to find their flaws, or worse, try to expose those flaws in public, we do both others and ourselves a disservice.
I don't want my instructor to lecture me on morality, but I do want and expect a compassionate and informed answer to a basic question on morality as it relates to martial arts, and I do expect instructors to comport themselves with the dignity and morality befitting any good teacher. I must always strive to do the same.