I'd like to give an analogy I recently thought of to compare Fi and Fe. (Or any other Jungian functions, but this is the bone of contention, here.)
We keep on trying to say what Fi "is" or Fe "is." Well, they aren't "is"-able, not in the way we usually think. I tend to fall into the functional language that is common on the forum, because I regard it as shorthand for a much more complex concept that doesn't admit any verb I can think of in the English language.
Fe and Fi might best be thought of as "frames." These frames, in turn, determine how one perceives this, that or the other thing. These different frames can look at the same thing, and talk about the same thing, but what ends up being seen and said sounds completely different, even if, for example, people of both frames are equally moved by an emotional situation.
The analogy:
According the the special theory of relativity, how one perceives lengths and distances and the flow of time, and even
simultaneity itself, is different. Let's say we have a "stationary frame" and call it Fi. And a "moving frame" and call it Fe.
Now, according to the theory, one can have identical rulers and clocks in both frames, yet still take different measurements of the same thing. The Fi frame sees the Fe frame as "shorter" in the direction of motion, and perceives the Fe clock as going "slower" than Fi's own clock. If there are two events, A and B, that happen at different points in space, it is possible for the Fi frame to measure that A happens before B, while Fe "erroneously" claims that B happens before A.
It gets better, though: let's re-label what we called "stationary" and "in motion" The Fe frame feels just as stationary as the Fi frame. Moreover, the Fe frame sees the Fi clock going slower. And the Fe frame sees that the Fi lengths are "shorter" than the Fe lengths in the direction of motion.
So you get arguments like:
Fi: Your clock is slower.
Fe: Pardon me, but it is your clock that is slower, not mine.
Fi: What are you talking about? It's self evident that your clock is slower, AND you're shorter, too!
Fe: Who's calling who shorter, pipsqueak?! You don't have a clue what you're talking about. You're shorter!
Fi: *fumes* How can you be so unreasonable?
Fe: Yeah, right, as if *I* am the one being unreasonable.
Sound familiar?
There's a way out of it, but it's difficult. Each needs to refigure things out in the others' frame. In special relativity, this is easy, because Einstein (through Lorentz) gave us the formula. We can do the math, and prove that, after all, neither the observer in the Fi frame, nor the one in the Fe frame, is being unreasonable.
But when dealing with MBTI/Jung, there's no math we can do. We each need to make an effort to bridge the gap ourselves, to put ourselves in the "other frame," if only for a little while. Our only clues come from those in the other frame, to whom we need to listen closely and hopefully we manage to find a way to apply both.
When we're doing it right, I believe it would sound something like, "How can that be true? How are you perceiving things such that you would come to that conclusion?" as opposed to, "There's no way that can be true."