Anyone who believes that "maximizing one's own utility is contrary to utilitarianism" is fundamentally confused as to the standard meaning of at least one of those terms. Not knowing which one, however, I'm not sure what I can say to make the matter more clear.
Maximizing one's own utility is practical rationality. Maximizing the world's aggregate utility is utilitarianism. The two need not the the same, and in fact can conflict. For example, you may prefer to buy a cone of ice cream, but world utility would be bettered more effectively if you'd donate that money to charity instead. Buying the ice cream would be the rational own-utility-maximizing thing to do, and donating to charity would be the utilitarian thing to do.
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