According to the professor, why does Sartre reject most Western approaches to ethics?

Listen to part of a lecture in a philosophy class.
    Professor So what is ethics? Well, ethics is the study of what is right and wrong, good and bad. The great ethical thinkers have concentrated on what makes an act right, what makes it wrong and what are our duties, what are our obligations. These are the typical questions that you encounter in the study of ethics.
    Let’s introduce Jean Paul Sartre—the French philosopher. It is pretty clear that Sartre rejects most of the approaches to ethics in the history of Western philosophy, approaches to ethics that try to ascertain the fundamental principles of morality. For example, the English philosopher Joan Stuart Mill in the 19th Century did exactly that. He said what is the most basic and fundamental principle of right and wrong, and he came up with his theory of utilitarianism. Utilitarianism claims that an act is right if it promotes the greatest happiness for the greatest number of people, so if the way a person chooses to act benefits as many people as possible, if no other action could benefit more people, then the person has acted rightly. Mill’s theory and other major teachings in Western ethics seek to provide principles, rules that we ought to follow, basic guidelines for human action.
    And Sartre rejects this emphasis on rules. To explain why, he gives an example that has become very famous: a young Frenchman during the Second World War is trying to figure out what to do. This young man lives alone with his mother, and his mother relies on him, so he feels an obligation to take care of her. But on the other hand, France is at war, so the man also feels an obligation to help protect his country. What should he do? If he stays home the benefit is pretty certain, he could continue to help his mother, but she is only one person if he joins the French resistance and helps defend his country, he could probably help more than one person, but then again, he might die in the first moment of battle and in effect, help no one at all. Possibly he could help a lot of people by joining the resistance, but not definitely. So Mill would tell this young man: do what will promote the greatest happiness of the greatest number. But which of these two actions—staying home or joining the resistance—would promote the greatest happiness of the greatest number? There is simply no way to answer the question.
    You could say, well, maybe there is some other rule or principle that would work here; what if I am simply out for my own game? I am going to do what is in my best interest. Would that tell our young Frenchman what to do? So, what is in his own best interest? To help his mother, or to help is country? Again, there is no way to answer the question based on principles alone. Sartre actually tried to answer this question, using many different ethical principles. Well, the result in each case was that there are no ethical principles that will settle the issue for the young man. Finally, the man just has to decide and he must take responsibility for his decision. That is the tough reality of it.
    Ethical philosophers from the beginning of Western thought have offered us principles, but these principles don’t give us real decision making procedures. And they don’t address the idea of taking responsibility for our actions and the consequences of our actions. Taking personal responsibility, being held accountable for what we do. This is a core concept in Sartre’s philosophy.
Student: But can we interpret Mill’s ethical theory to mean that there are multiple choices that are all equally good?
Professor: Well, certainly you might claim that. In some cases, it’s ethically or morally indifferent what you do. Neither choice is preferable; each one is permissible. But still, "What do I do?" Knowing that an act is permissible is not telling me to do it. I still have to choose, I have to pick one option over another. Of course the case of the young Frenchman is not an everyday experience, but it certainly drives home Sartre’s point. All of us are in a predicament of making decisions every day, and most of us probably think there is a right and a wrong, that there is some ethical principle out there that will tell us what to do, but that sort of principle in itself doesn’t give us much practical guidance. Sartre would argue that this is true in all cases.