Sympathy is appropriate for a leader, but empathy is dangerous. People tend to use sympathy and empathy interchangeably but there is a difference.
Sympathy is understanding and appreciating another person’s situation or perspective. Sympathy helps you appreciate a problem but keep emotions in check while you ponder a decision for the group.
Empathy leads you to dramatically and fully identify with one person, or one sub-group — including emotions. Yet a leader in a group can’t have empathy with all of them. Empathy is dangerous because you’re likely to make a decision which is not best for the whole group.
Consider the case of a judge managing a trial. She can have sympathy for both prosecution and defendant, but empathy could easily undermine her ability to make an impartial ruling.
A leader needing to make tough decisions is wise to use sympathy and guard against empathy.