I can't count the times people have told me "How dare you, you think you know me so well? I don't even know myself that well so there's no way you do.". I usually respond with something about how self aware they think flies are.
so... I'm gonna go out on a limb and say that clears everything up, right?
To the original post... I think I see how everyone else is pretty well (if I misjudge, things go badly very quickly because I'm a lot more open with my feelings than your average INTP it seems), but it's really, really hard for me to tell if I'm right. The reason is because most people don't like who they are. At least, I'm sure I don't like who I am... and that fact is the only thing that keeps me from harshly judging other people, because when it comes down to it they're not usually very good people either. I have a tendency to take the character flaws I think I see for granted in my analysis and actions towards them, though, and when they catch on I get very, very different replies. The people who I thought originally were honest with themselves and want self-growth tend to take suggestions to heart, usually understand the logic behind my accusation, and we're both better off for it (even one of my friends who's an ESFJ, believe it or not). The people I thought originally were faking their character I can't keep my mouth shut about, but they get really mad and defensive and deny it. So this reaction either confirms my analysis that they're fake people who don't like the truth, or it means that I'm way off and they dont have whatever unpleasant quality it was that started the argument.
The people who like the criticism, irrelevant of personality type, tell me I'm very perceptive... but due to my introvertedness they never get to see me analyze anyone else. The ones who get offended and defensive tell me I'm presumptuous and arrogant. If I had to judge myself I'd say I'm pretty darn accurate... but I think that's an arrogance common to the INTP type.
As far as emotions go, I think, like lor suggested, I got a lot better at it over the past couple years when they became one of my primary topics of interest. It didn't hurt that I felt a lot of depression and despaired during some of that time too, so it got easier to see moods in other people (trying to hide symptoms from the family and stuff really makes you attuned to what those symptoms are). I'm in a similar boat to you, though. I still really don't know how to relate to people who are upset. The only things I've picked up (which are really, really not many) I've taken from other people. I couldn't tell you why it's helpful to hug someone who's in tears, but I asked some friends and watched others, and apparantly it is. It really depends on the person too whether it's helpful to know where their feelings are coming from, or if they just want to be told that it's natural. I have nothing really to base this off of but intuition... but I think that most people are the latter. Starting off with an "ahh I'm so sorry... I had no idea your family was in such trouble" and a hug (depending on if they're the type to do that... I know that none of us probably are, but if you're gonna step out of your comfort zone, the time to do it is when someone's in tears and coming closer to you than is normal) will usually make any well-thought out intellectual advice go a lot farther.
At least... that's my current take on it. It comes a lot more from observation and conversation than experience... but I mean... haha if you put more faith in experience than theory you probly wouldn't be here anyway. And, I can at least tell you I've never had anyone leave in a worse mood than when they came since I started looking at things like this... the same cannot be said of when I used to just do what came naturally, analyze and explain.