How can you know their feelings, if you do not know the reasons for their feelings? Empathy as understanding someone's frustration requires you to first know that someone is actually frustrated (otherwise you are just imagining).
Have you had a bad day? If so, then you can empathize with their bad day without knowing their reasons.
Personal note, empathy is SO much easier for me the less I know. If they share their problems, I instinctively start dissecting and analyzing their situation.. It's easier to just recognize suffering and to try not to contribute to it or lessen it.
I don't mean to be dismissive, but I really don't understand what you're trying to say. My understanding is that we are talking about face-to-face interaction with a clearly frustrated person. Why wouldn't you know they were frustrated?
>some times people are having a really bad day for reasons you can't see
It's not clear how you know someone is having a "really bad day" when you explicitly rule out knowing the reasons why the person is having a really bad day.
Maybe they told you they are having a really bad day? That is fine and fairly easy to empathize with.
Maybe you are just assuming someone is having a really bad day because of how you perceive their actions?
You are using empathy in a different sense than (I think) most people are in this thread. I'm no psychiatrist, but usually when I hear people discuss empathy (or more often, someone's lack of it), they mean it almost in the sense of a lower-level mental process. Empathy is more than just feeling bad for random strangers who feel bad themselves- if anything, that's just a side effect. Empathy is the thing that makes you feel bad when you hurt someone else, even if you had a good reason for hurting that person. Empathy is the thing that allows you to sense other people's internal states- it's not magic or psionics or whatever, it's just your subconscious maintaining a background thread that is paying attention to signals from other people, and communicating those signals to you by internalizing a distant echo of what that background thread has determined that they must be feeling. It's fundamental to human interaction and cooperation and is (IMO) one the biggest drivers of the development of civilization.
A sociopath is an adult who never developed this facility. Children don't have empathy- it's one of the things that makes them children. That's why some kids do things like torture or kill animals...in their minds, those animals aren't creatures with sensory experiences like themselves, rather those animals (or even other people) are perceived as meat robots, for lack of a better term. Lacking empathy means when they hurt someone, they don't feel anything themselves because there is no background thread in their subconscious reminding them that the person they are hurting is another thinking, perceiving, feeling being like themselves.
Psychiatrists can't diagnose someone as a sociopath until they're 18, by which time people's brains are expected to have developed some capacity for it. People on the autistic spectrum also have a lesser capacity for empathy, that's part of what defines them as being autistic. They can't perceive subtle social queues because of this lack of empathy.
There are plenty of people who are self-aware, functioning sociopaths- they've spent their lives having fundamental social problems, never relating to other people the way that everyone else seems to be able relate to each other. At some point in life they discover that their cognitive development wasn't perfect, and once they understand the nature of the issue they can compensate by making a conscious effort to do so. There are also plenty of sociopaths who never made this leap, and basically all you can do is stay as far away from them as possible, because who wants to deal with someone who thinks you're a meat robot?
In the context of this thread, people aren't talking about sociopaths or anyone with autism/Asperger's/etc., but imagine a seemingly normal adult with underdeveloped empathy- it manifests in all sorts of ways, from being jerks to retail employees to stiffing waiters to just being an unpleasant person to interact with. Those people don't realize they have an underdeveloped cognitive process, they just go through life wondering why so many people think they're jerks, and saying things like "99% of humanity is way too sensitive". I would attribute a lack of self-awareness to a lack of empathy as well- if someone is incapable of seeing themselves through other people's eyes, then they have no way of gauging their own behavior or feelings.
In the context of this thread, I don't understand why you brought up either sociopaths or autism/Asperger's/etc., especially when you specifically disclaim it in your last paragraph.
I think the problem with this conception of empathy is that it seemingly derives solely from the person experiencing it. This type of empathy requires a subconscious background thread to be keeping track of signals which may or may not exist in the external reality. If it is at all possible to know (whether or not such signals exist), it would appear to at least require some communication. Otherwise you are just trying to make inferences off of what you observe, which is probably a near insignificant amount of what the person you are supposedly empathizing with has observed (leaving the question: How do you actually know that the things you are feeling are actually, exactly the same as what the other person is feeling?). I believe this definition of empathy allows people to feel good about themselves, that they are not a sociopath, while still allowing for the possibility that the empath is not actually feeling the same thing as their target.
