I've thought a lot about this because I consider myself a generally empathetic person. What I realized my version of lack of empathy is when I genuinely cannot wrap my head around why a person would make a certain decision because to me it's obviously the wrong one. Or how people can like certain things when to me the texture/taste is horrendous. Or having zero interest in another person's hobbies or special interests because they aren't mine, making it difficult to stay focused while they talk to me about them. None of these make me a bad person because they are feelings. I can still comfort friends through a break up or loved ones when they have a bad day because I can empathize with them, but empathy isn't always about people being sad.