Pluming himself on his cleverness, he refuses to take others' advice.
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自恃 is a literary, often pejorative verb. The pattern 自恃 + (quality) means 'to overrely on / be cocky about (one's quality)' - e.g. 自恃才高 (overconfident in one's talent), 自恃有功 (presuming on one's achievements).