So, it's clear we Fi doms (or NFPs) have a different relationship with our emotions. In another thread I compared our relationship to emotions as being a little like going through the day with a relatively well-behaved pet by side. You know your pet well, and you know it reacts to things that you may not consciously perceive. It's entirely possible for your pet to become unruly or distracted ("Squirrel!"), but mostly it functions as a second set of eyes and ears. In a way, I feel a certain amount of affection for my emotional state, because it does almost feel like having a companion throughout the day.
So our emotions function as a constant barometer that is always providing some feedback. Our feelings are often the result of all kinds of subconscious judgment. Our emotions aren't always "right"— for example, just because I feel irritated at someone doesn't necessarily mean anything about that other person. Maybe that person has similar mannerisms to someone else, and the association is triggering the feeling. Still, one never feels things "for no reason." There's always
a trigger, an association or a subtle judgment that sets them off. Fi helps you monitor your emotional state, so when that state changes it's a reason (for an INFP, anyway) to ask "why?" Over time, you get to know what causes changes in your emotional state, and then you can react accordingly. In fact, you eventually use that self-knowledge to manage your own emotional state.
So, perhaps some of the above helps explain why NFPs sometime tell others "I'm perceiving you are feeling X." There's (from our perspective) likely important information somewhere in that feeling. Your not managing it is a bit like having to sit next to someone who is ignoring their barking dog or crying baby. It muddies our own emotional awareness, because we're distracted by data from you that we have to try to ignore. When you say, "I'm not feeling X" (which we have to trust, because we can't really know your emotional state), it means we have to go forward having to consciously keep ignoring that ongoing perception.