You are in the midst of a power play, and this employee is playing you. He threatens to leave, and you grant his wishes. This is ultimately a formula for widespread resentment from others in your organization. It is also a formula that encourages repeat performances of his threatening act and actions.
Most employers would not tolerate any kind of threat from an employee. It will be helpful for you to try to figure out why such behavior is acceptable to you.
You state that he is a very good employee. Presumably you are describing his technical skills, but there is more to being a good employee than that. A good employee certainly has the skills, but he or she also shows teamwork, loyalty, and commitment, among other things. Your employee is not very good when it comes to this.
You should give him direct feedback on his inappropriate demands and the consequences if they continue. The consequences can range from discipline to termination. Secondly, stop giving in to his demands. And finally, start training or searching for a replacement. At some point, he is going to carry out his threat, and you should be prepared to carry out yours as well.
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