John Keats chose a sonnet in response to Chapman's Homer because it was his favorite poetic style at the time.
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 "On First Looking into Chapman's Homer" while still training to become an apothecary, Keats studied and experimented with the English sonnet to an extent his brothers feared "he would destroy himself if impeded to write poetry".
