Empathy for many is quite hard to achieve. Most confuse it with Sympathy, and that generally doesn’t get received the same way. People want Empathy, not Sympathy.
Empathy is much easier when you have experienced something yourself. Grief, deep grief is something that some will never acknowledge; others will find it difficult to cope day to day. Be it a broken leg or someone who has died, empathy can be drawn from anywhere. It’s understanding. You don’t feel sorry for or pitty someone, you understand their sorrow and support them. A key difference. A “there there” pat on the shoulder is daft. A full embrace and a cry is normal.
Don’t try and tune out your emotions. You’ll find yourself bitter and cold. Embrace emotions and personal experience. Support people.