I can't say I ever thought I felt what someone else was feeling, so maybe I just have no empathy. I also don't ever get angry, so maybe that's related. (I make one exception for misbehaving computers with no clear reason or solution, but I'd call that frustration.)
So generally, I agree with the author that understanding others and responding in supportive ways is much more useful than feeling what you think they are feeling. I am just skeptical that anyone would argue, and I would be surprised if that's what the quoted people had in mind.
I was getting the sense that the author had decided to use a twisted definition of empathy, and came to a series of faulty conclusions because of that. At the start, the author says "When I say empathy, I mean sympathy", in which case... the term "sympathy" should be used. In my experience, people don't use them interchangably; sympathy is feeling sorry or happy for someone, empathy is understanding where (and why) that person is coming from. Or at least, trying to.
I got through a third of the article and it really started shaping up as "I don't like sympathy" rather than empathy; starting from faulty premises, the author gets to have his 'shock value' statement, but it's not accurate.
TLDR; Don't just mirror the feelings of those you love, understand their feelings and use that information in a truly helpful way.