If someone cries out in pain, I have no doubt of their experience. It is this phenomenon, which is not formally meaning, that I am calling "empathy."

Excuse me for taking this apart some more:
The first sentence implies that this is an unfailing, quasi-automatic reaction of you as a human being.
But the remainder of your argument suggests that you regret the very fact that empathy is not general, but has to be taught, and can be "manipulated". A quality which would be inborn/instinctive could not be considered part of ethics, because, as I see it, ethics is about conscious social behavior.

Now something rather provocative: Is there really a categorical difference between the first, purely emotional reaction on hearing someone cry out in pain on one hand, and witnessing a valuable object (like a brand-new car) going to pieces in a crash, on the other hand?
What I want to demonstrate is a warning not to stylize every pinching gut-feeling as empathy.