Lets be clear...being empathetic has nothing to do with your personal emotional state. It is not about feeling sorry for someone else, nor is it about the level by which you give in to your team members demands. Empathy is about connecting with someone on their level in relation to what they are experiencing; it is a level of awareness, understanding and supporting another person.
I believe in being vulnerable and am confident enough to say - I may not be sympathetic, I am not apathetic, BUT, I AM empathetic. This is a characteristic I have cultivated over many years, and it has definitely taken practice. I believe this is something that comes easier with confidence, experience, maturity, and an ability to listen; heck, it may even take being wrong a few times before you recognize that gaining a perspective counter to your default is a great learning opportunity.
A leader must assume the best in their team, however bad behavior must also be addressed, and in some circumstances must be addressed swiftly. The key is to address the behavior not the person, AND once it has been addressed, the leader must have the confidence to move forward from it and trust it will be corrected. To continue addressing the same behavior over and over insinuates a problem with the person, which, in and of itself, is a demonstration of lacking empathy.