When an employee gets confrontational and threatens to quit in order to get a salary hike, promotion, or organizational change he demands, let him quit.
First, listen him out and consider his demands seriously. Beyond that, be resolute and ask the employee to stop threatening or feel free to leave should he disagree with your decision and insist on his demands. Communicate with the employee in writing and document the disagreements to protect yourself and your organization against a claim for wrongful termination.
Let the employee quit even if he is a valuable performer. Nobody in an organization—not even the leader—should be indispensable. The long-lasting success of an organization should never be contingent on the performance of one individual. (I cannot stress more how important employee succession plans are to an organization.)
Look, the first time you yield to the demands of an employee who threatens to quit to get what he demands, you set a dangerous precedent. Others in your organization will assume that they too could threaten to quit to get what they want. You could lose control over your organization if you concede to employee demands thoughtlessly.