Impossible to say what was behind any specific request, but what is generally meant by “Have a little emapathy” and its kin is : “Stop criticizingjudging/etc. or communicating with the individual being discussed that sharply, because we feel the individual has good reasons/a good excuse/a good justification for sympathy and/or some leniency here.”
I think the author understands that "have a little empathy" is a request to modify their behavior, but expresses their frustration that the request is unclear and (in the author's experience) the requestors won't clarify the request.
Contrast this with the conversation we're having now where I requested clarification on your initial comment, and you thoughtfully provided it.
But to your point, there's an innate "getting it" where your level/expression of empathy is roughly in-line with people you interact with, and if you don't have that, you need to do work to "get it", which is what the author did.
We can compare empathy to other practices that can benefit from innate understanding. Some people "get" poetry, math, music, long-distance running, etc. and we can all work to "get" them, but in my experience, it's never quite the same.
I _don’t_ think that empathy has anything to do with it though.
Behaviour modification yes, but that is “stop talking so critically”. Or “don’t be so harsh” or “give this person special treatment”. WHEN to do that might be key here—perhaps the colleague’s husband has cancer, or their child missed school 3 days this week with the flu, or their project wasn’t productionalized/their new to the role/etc—and so a blanket “don’t talk so harshly” isn’t called for—instead what is really desired is social calibration.
But instead it seems everyone is getting caught up on the literal interpretation of this figure of speech instead.
