I'm not wrong.
There is no neutral about not caring about someone. You either like or dislike them whether you care about them or not.
You honestly have no clue about feelings toward people and whether you can care about people or not?
The fact is when you don't care for an object you don't have feelings toward it.
Disliking someone is a feeling.
If I say "I don't care for your posts" I don't have any feelings toward any posts of his.
Now, If I say I don't care for any of your posts, and you dislike his posts, then that is a feeling towards him.
Same applies when it's toward a person.
If you don't care about someone it's meaning that you don't have emotional feeling about them because you don't care for them.
You dislike Lord Tony, you may blatantly ignore his posts like a richard but you still care enough to hate on him.