I am not an expert, but as I understand it Fi is knowing what is good/bad or right/wrong. It is an evaluative process that is highly subjective (meaning: differing among individuals).
So if Ne thinks in global fashion, Fi pulls us down to earth and makes us think okay what is good/bad or right/wrong for THIS situation/person/whatever.
But if Ne and Te act without Fi, I can imagine that as being - this is my global generality now let's do this shit and screw it!!!!! RAWRRRRRRRRRR! Yeah, baby, I got this!!!!!!!!!
Therefore Fi makes us question/evaluate/put the global generalities to the test.
Um, let me think of an example. (Probably going to be a crappy example because I admittedly didn't really think this through - just winging it).
Healthy Harmony of Four Functions:
Ne: Explosion of ideas on how to teach concept X.
Fi: What is really good for THIS group with this dynamic and these individuals?
Te: What do I need to implement this idea? How shall I go through with it?
Si: How have I taught this before? How did it work? Is this group similar? Can I extrapolate a reasonable chance of success as compared with the past?
Unhealthy Disharmony/Lack of Strength
Scenario A: Tired/Lack focus
Ne: Explosion of ideas.
Unhealthy Fi: Don't know which to use.
Te: PICK ONE DAMN IT.
Si: Fuck, nothing ever works.
Scenario B: Don't consider the group
Ne: Explosion of ideas.
Unhealthy Fi: That will work.
Unhealthy Te: Don't think it through/don't prepare right.
Unhealthy Si: Well, shit, that lesson sucked ass. Shit. Why didn't it work? It worked with the OTHER group.
Unhealthy Fi: That group is just stupid and shitty. They are the problem.
Unhealthy Te: Fuck 'em.
Scenario C: Use an improper method - most dominant functions are silent. Only aux speaks with gross overtones. -> At home, safe, after a bad lesson
Unhealthy Fi: What the fuck is wrong with these dumb assholes?
Unhealthy Se: Tell em who's boss. These little fuckers need a lesson. A REAL ONE!!!!! RAWRRRRRRRRRRRRRRRRRR!!!!!!!!!
Healthy/weak Ti: Doesn't make any sense.
Unhealthy Fi: Yeah, because these idiots are bad, wrong, stupid, dumb, idiotic, moronic....
Unhealthy Se: Yeahhhhhhhhhhhh baby and now I am gonna kick some ass.
Healthy Te: Probably not the best idea.
Unhealthy Se: Okay. I will yell. Get their attention. Hey over here you little dumb fart. Yeahhhhh I am talking to you. STFU AND LISTEN TO MY ASS!
Healthy Te/Ti/weak: Uhhh - what are you doing?
Unhealthy Se: SHUT IT!!!! SHUTTTTTTTTTT ITTTTTTTTTTTT! *throws temper tantrum*
Unhealthy Ni: I definitely see someone's going to lose their job over this.
Unhealthy Fi: I am bad. I am a horrible teacher. I am a loser. I suck at life.
Unhealthy Ni: Yeah, you're going to die cold and alone.
Healthy Te: Um, what are we even talking about here? HELLO?!?!?!?!?!
Oh, I can give a billion examples, but I think you get the point.
If I am on the wrong track, please let me know. But that is how I understand it.