Karl Wojtya (aka, John Paul II) deftly charts the collapse of utilitarianism into egoism in Love and Responsibility (37-39):

Utilitarianism makes pleasure the overriding aim of human action.

But pleasure is a momentary good, and a good only for a particular person.

A utilitarian might attempt to maximize the pleasure of another, but, if consistent, only insofar as and as long as it gives pleasure to the utilitarian.

When the other person ceases to give pleasure in his pleasure, “I shall then . . . seek to eliminate the other person’s pleasure because no pleasure for me is any longer bound up with it - or at any rate the other person’s pleasure will become a matter of indifference to me.”

Thus, “a subjective understanding of the good (equating the good with the pleasurable) leads directly, though there may be no conscious intention of this, to egoism.” The only escape is to recognize a common good that can unite the persons.

Wojtyla is especially interested in how this dynamic plays out in sexual relationships. He thinks it produces a “paradoxical pattern”: “each of the persons is mainly concerned with gratifying his or her own egoism, because this can provide the opportunity for such gratification - and just as long as it does so.” Both persons are reduced to “tools,” since “if I treat someone else as a means and a tool in relation to myself I cannot help regarding myself in the same light.”