Part of his advice is to take genuine interest in other people. What you may be interpreting as insincere, is someone trying to take genuine interest but failing miserably.. hence the practice part. I have found myself in those situations to be honest.
It isnt that they dont care about the subject, its that you care enough about the person that you try to understand why they like the subject.
Some people interpret this to mean you have to fake interest in the subject, or you have to be honest that you don’t like said subject but it can also mean you take interest in the subject simply because the subject is of interest to the person you’d like to be friends with.
You're right, there may be times I don't notice. I have no data to prove that.
IME, being in the moment and my body instead of in my head made it apparent that we aren't as clever as we think we are in social situations.