John Keats chose a sonnet in response to Chapman's Homer because <em>it was his favorite poetic style at the time</em>.
Writing sonnets allowed him to express all the emotional power so natural to the romantic poets he derived inspiration from, e.g. Lord Byron and Leigh Hunt
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Between 1815 and 1816, around the time of publication of <em>"On First Looking into Chapman's Homer"</em> while still training to become an apothecary, Keats studied and experimented with the English sonnet to an extent his brothers feared <em>"he would destroy himself if impeded to write poetry"</em>.