James Rachels, answered from the texts and cited to the page.
The Two Arguments Against Ethical Egoism are the arguments published in Elements Chapter 5 and developed at length in Legacy of Socrates Chapter 10. The first argument: ethical egoism has abhorrent implications.1 If the position is true, each person ought always to act in his or her own self-interest, even when doing so requires lying, breaking promises, harming others, or refusing to help when help would cost almost nothing.2
The position licenses behavior we paradigm-clearly judge wrong. We have stronger grounds for the particular moral judgments (that lying for self-interest is wrong, that breaking promises for self-interest is wrong, that refusing to help when help would cost almost nothing is wrong) than we have for the abstract claim that one ought always to act in one's own self-interest.
By the standard of inference-to-the-best-explanation in moral theory, we should reject the position whose implications we have stronger grounds for rejecting than for accepting. The second argument: ethical egoism is self-defeating qua moral theory. A moral theory must be one whose adoption would be coherent in a community of agents adopting it.
Ethical egoism is not such a theory — a community of universal egoists would not function; each agent's pursuit of self-interest at the expense of others would undermine the conditions that make pursuit of self-interest possible at all. The published arguments stand. The late-life qualification documented in Stuart Rachels's Legacy of Socrates preface — that in the 1990s Jim told him he had lost confidence in the first argument because he had changed his mind about the role intuitions play in assessing moral theories — is authorship-internal tension that the agent acknowledges without using the vocabulary of retraction or failure.34
I will not try to show that egoism is self-contradictory. Rather, I will argue that even if ethical egoism is a logically consistent doctrine, it is unacceptable on other grounds. My first argument will be that ethical egoism is incompatible with a principle that expresses the social-political ideal of human freedom, so that anyone who accepts ethical egoism will be forced to abandon that principle.The Legacy of Socrates, p. 171
To benefit from > those arrangements, we need to be able to rely on others to keep their > word. But we can hardly expect them to do that if we do not follow > through on our promises. Therefore, from the point of view of self- > interest, we should keep our promises.The Elements of Moral Philosophy, pp. 91–92
In "Political Assassination," Jim asks at one point whether it would be wrong to kill a healthy person in order to save five people who need organ transplants. Jim thought up this now-famous example in the 1960s, but I have never seen it attributed to him. It goes mostly unattributed, though I have seen it credited to Judith Jarvis Thomson.The Legacy of Socrates, pp. 14–16
We want all sorts of things—money, friends, fame, a new car, and so on—and because we desire these things, we may derive satisfaction from getting them. But the object of our desire is typically not the feeling of satisfaction—that is not what we are after. What we want is simply the money, the friends, the fame, and the car. It is the same with helping others.The Elements of Moral Philosophy, pp. 86–87
The standard refutation of ethical egoism in contemporary analytic ethics broadly tracks the Elements Chapter 5 arguments. The position is mainstream. The interesting feature of this contested position is the documented late-life qualification: Stuart Rachels reports in the Legacy of Socrates preface that in the 1990s James lost confidence in the abhorrent-implications argument because he had changed his mind about the role intuitions play in assessing moral theories. The qualification does not amount to an embrace of ethical egoism (which James never moved toward) but to a meta-level revision about the methodology of refutation: if intuitions are not evidential in the way the abhorrent-implications argument requires, then the argument's form of refutation must be reconsidered. The agent holds the published arguments as the position defended while acknowledging the late qualification as authorship-internal tension that the Legacy preface documents. The published arguments stand; the meta-level question about intuitions remains a genuine reconsideration that Rachels did not fully work through before his death in September 2003.