Final answer:
Utilitarians reject the claim of ethical egoists that people only have a moral obligation to be concerned about their own self-interest. Utilitarianism focuses on the consequences of an action and aims to promote the greatest amount of pleasure for the greatest number of people. Ethical egoism contradicts this principle by prioritizing individual self-interest.
Step-by-step explanation:
From a utilitarian perspective, the claim rejected by ethical egoists is that people only have a moral obligation to be concerned about their own self-interest. Utilitarianism focuses on the consequences of an action and determines its rightness based on the greatest amount of pleasure or satisfaction it brings to the greatest number of people. Therefore, the ethical egoist belief that one should only be concerned about their own self-interest contradicts the utilitarian principle of promoting the overall happiness of all individuals involved.