Lewis begins by explaining how such a system might work. In this system, a person can essentially discard all thoughts, including their own, as subjective. This doesn't work with what is called theoretical reason, or scientific reasoning, because as Lewis writes, a person must "assume the validity of his own logic...even in order to prove that it is merely subjective."
Practical reason, or the judgment of good and evil, is a different matter. It is arguing against the subjectivism within the context of practical reasoning that Lewis spends a majority of his time in this essay. We are told by society that "to say that a thing is good is merely to express our feeling about it; and our feeling about it is the feeling we have been socially conditioned to have."
This is, of course, very dangerous. If right and wrong are completely subjective, then we lose the basic structure of our society. In my mind, our society is built on some basic principles, such as our inalienable rights. These basic rights given to all and acknowledged by all prove that there must be a basic law or idea behind them all. A "new" form of morality or a "new" idea of truth must will still have its basis within this basic law. How then, do differing views of morality come about? It must come in the twisting of this traditional morality. By changing one aspect of the traditional morality, a "new" ideology is made, but it must be ignored because it uses the very thing it tries to disprove in order to prove itself. I tried to think of an example of this, but it is so illogical that I can't even think of one.
Overall, I think that we must remember that there is a definitive right and a definitive wrong. These may be difficult to see, but they are present nonetheless.
(note: I may write more on this essay following our class discussion. These are merely my own meager thoughts.)