In a manner characterized by egoism or excessive self-interest; in a selfish way based on egocentric philosophy.
From egoistical plus the adverbial suffix -ly, creating an adverb form that describes how an action is performed from an egocentric perspective.
When you use 'egoistically' instead of just 'selfishly,' you're making a philosophical claim—suggesting the person actually has *reasons* for their selfishness, which is weirdly more insulting.
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