The right read here is to realize that psychology alone is not the basis for moral concern towards other humans, and that human psychology is, to a great degree the product of the failure modes of our cognitive machinery, rather than being moral.

I find this line of thinking to lead to the conclusion that the moral status of humans derives from our bodies, and in particular from our bodies mirroring others' emotions and pains. Other people suffering is wrong because I empathically can feel it too.

"Morals" are culturally learned evaluations of social context. They are more or less (depending on cultural development of the society in question) correlated with the actual distributions of outcomes and their valence for involved parties.

Human psychology is partly learned, partly the product of biological influences. But you feel empathy because that's an evolutionary beneficial thing for you and the society you're part of. In other words, it would be bad for everyone (including yourself) when you didn't.

Emotions are neither "fully automatic", inaccessible to our conscious scrutiny, nor are they random. Being aware of their functional nature and importance and taking proper care of them is crucial for the individual's outcome, just as it is for that of society at large.