Well, that's a bad argument, this is all a guess on your part that is impossible to prove, you don't know how empathy or the human brain work, so you don't know it isn't computable, if you can explain these things in detail, enjoy your nobel prize. Until then what you're saying is baseless conjecture with pre-baked assumptions that the human brain is special.
conversely I can't prove that it is computable, sure, but you're asserting those feelings you have as facts.