Why is Jim so vehement in his dislike of King Soloman? Through the stand Jim takes, Twain is making a statement concerning antebellum society's common stereotype of the slave.
Jim dislikes King Solomon because Jim feels that Solomon's famous stroke of wisdom (offering to cut a baby in half) is actually a stroke of idiocy.
This is an ironic moment. King Solomon, as the proverb goes, was presented with two women who both claimed to be the parent of the same baby. The king suggests to the women that they cut the baby in half to settle the dispute, giving each mother half. One woman agrees to the terms and the other woman, appalled at the idea, says she would rather have the baby live and be raised by the other woman instead of being killed.
King Solomon then awards the baby to the woman that wanted it to live, saying that she must be the true mother. Any true mother would want her child to live and would not treat the child like a piece of property.
Jim does not see wisdom in this anecdote. He sees folly. He does not understand that the baby was never cut in half, but instead fixates on the suggested solution. He does not mentally work through the entire problem and so fails to understand it.
This is ironic as Jim is judging wisdom unwisely.