It seems to me you're committing an is/ought fallacy. The GP was was describing his/her actual feelings on the matter, not the idealized feelings you seem to be recommending.
Most people ought to instead focus on cultivating sympathy, which is the intellectual realization of another's suffering, and turning that sympathy into action.
If I stub my toe you don't have to feel that pain to empathize it, you have to understand what it feels like to suddenly be in pain. Sympathy in that situation would only require recognizing and pitying someone who is in pain, without necessarily understanding it.
Merriam-webster defines empathy(https://www.merriam-webster.com/dictionary/empathy):
> the action of understanding, being aware of, being sensitive to, and vicariously experiencing the feelings,
Notice the 'and vicariously experiencing'. If there is no experience, it is not empathy. Stop using the word to mean something it is simply not.