Antonyms for "taking kindly to" would include phrases such as "dislike," "harshly reject," "resent," or "take offense to." These terms imply a negative reaction towards a person or situation, as opposed to the positivity of "taking kindly to." A person who does not take kindly to something may be seen as closed-minded or unwilling to accept new ideas, while someone who takes kindly to something may be viewed as open, receptive, and respectful. Differences in communication styles, personal beliefs, and cultural backgrounds can all factor into whether someone takes kindly or not to a particular situation or person.