empathy can be roughly divvied up into cognitive empathy (reasoning why someone is feeling a certain way) and emotional empathy (recognizing that someone is feeling a certain way)

Colloquially people think of the latter when they use the term “empathy”, don’t they?
The former is a deduction, not empathy, it looks like.

I meant the latter anyway.

By the way, I don’t think sense of injustice is necessarily rely upon empathy.