How does one give feedback to the most resistant and arrogant subordinate?
First, stop labeling him as resistant and arrogant.
Next, start with positive feedback. Tell them every time they do something well. Let the negatives go.
Meet with them regularly, just the two of you. Do it every week. Build up your relationship.
Then, after six or eight months, start pointing out when they could have done something better.
If only someone would make a podcast about these topics.....
I just want to say I fully agree with Tom´s advice, which follows from MT advice, on not labeling, building the relationship first, focus on behaviour (do not draw conclusions of intentions), positive feedback, then finally negative feedback.
Also do your DISC profile and evaluate his/hers, if you are of different-opposite communication styles you may be having a communication problem rather than a resistant and arrogant behaviour problem.