This is going to be fairly long. Worse, it's just one person's perspective (mine). Even worse, I'm starting with the least agreed-upon part of the spectrum - feelings.
H/T to UnaSpenser, whose fine diary was swarmed by people who wanted to meta-debate definitions rather than deal with any part of the problem.
Let's see if I can make the first distinction without running into too many reflex reactions.
"Feelings"
is used as a catchall word - it includes everything from describing a considered opinion about something where full knowledge is lacking - "I feel that you may not have considered this fully, because of x, y, and z.",
- to a description of thought processes which don't fall into a quantifiable set, such as levels of confusion or dissonance,
- to descriptions of a specific emotion that someone has
internally identified in conjunction with a situation or entity - "I feel sad when I think about x",
- to an
external assignment of an emotion to a particular comment, or phrasing, or word choice, - "you must be really angry to have said x",
- to a term which can be used - falsely - to dismiss an argument which is uncomfortable for the responder - "it's just your feelings getting the best of you",
- to a grossly pejorative comeback to a reply to (usually) baiting comments - "Did I hurt your wittle fee-fees?" (Note: it is possible to hurt a person. Feelings, on the other hand, do not themselves have feelings. A quick translation of the previous statement goes something like "Oh, goodie, I've managed to deliberately upset you and I'm probably going to get away with it".)
It's no wonder that, when we undertake any discussion of feelings, it tends to get turned into a fresh can of worms by those who are uncomfortable with the problems being addressed.
With that in mind, let's look at the other terms, which are slightly less prone to garble.
Knowledge and Belief
Leaving theology out of the mix, at least for the moment, knowledge can apply only to events which have already happened. To make the clearest possible case - I do not know that the sun will rise tomorrow. I know that it rose yesterday, and the day before, and the day before that. Or at least that the sky brightened through cloud cover at approximately the correct time on that day, and that when the clouds broke, the sun was in the expected position. I can reasonably presume that it will rise tomorrow, but I can't know it, even though I know the odds of it going nova between now and then are slim. I do not "believe" that the sun will rise tomorrow - I don't need to, because I have sufficient evidence of probability that I see no reason to postulate an unknowable factor as a significant part of the causal pattern that I've defined.
On the other side of the line, non-theological belief applies solely to future conditions - to events which are essentially unpredictable in the present. It is one of our great gifts as humans to be able to envision a specific future and work to build it - and a belief in that vision can make the difference between having it come to pass and it simply remaining a pretty dream. It's also one of our greatest problems, because conflicting visions of the future can lead to prolonged conflict, especially when resources are limited. If one accepts this definition, then simple statements like "I believe in science" or "I believe that such and such happened" become impossible to make, because the process and/or events are past or current, and thus subject to proof.
Unfortunately, "belief" is often used as shorthand for high levels of confidence, and then taken as a statement of theology or the existence of the supernatural by those who have learned to be more careful in their usage of the term. (Or, sometimes, by those looking for a good excuse for a fight. And sometimes it's hard to tell.)
Thinking vs. Opinion
When I say "I think x" I am stating my opinion. It is, or should be, subject to change as new data comes along, and no versus appears. In this, I am out of the mainstream. The Google definition is as follows:
Opinion: a view or judgment formed about something, not necessarily based on fact or knowledge
Since this is the generally accepted definition, anyone claiming an opinion may immediately become suspect, especially if the responder is looking for a good derail for the current topic.
To avoid this, it's possible to distinguish between
1.) what you know (data),
2.) how you and others have patterned that knowledge (thinking),
3.) what the pattern means or suggests to you (opinion), and
4.) what you a) think can (policy recommendations) or b) opine should (moral imperatives) be done about it .
Note that it's possible to share the same facts that others are working from and come up with widely (and wildly) varying opinions.
Emotion
This is the nitty gritty of the disagreements. Many people are totally uncomfortable with arguments which engage the emotions, particularly when their previous experience with strong emotion has been overwhelming, or has led to shaming, or shunning, or been connected with terminal confusion about the validity of emotions.
From a comment in an earlier diary:
The discussions on feminism over the last few months annoyed the hell out of me, not because I'm not a supporter of feminism, but because it was personal, not policy, that was the focus of discussion.
Just as all politics is local, so it can be said that all workable policy must first be personal. We don't make laws about things that don't matter to people, and to matter they must first engage people's emotions. It may be comfortable to speculate about disinterested altruism, but it's people caring about things that drives their acceptance or rejection over time. Positive emotional involvement is the sine qua non of positive change, no matter what the factual drivers may be. In an emergency, fear is a legitimate substitute, but fear burns out unless the emergency is artificially propped up.
We've fallen, I think, into the trap of assuming that negative emotions are stronger influences than positive ones, primarily because negative emotions tend to be expressed more forcefully. And, in a strange correlation, that if you begin to feel a strong emotion about something, it must be negative and should be avoided.
A note should be made about the difference between someone being able to experience a wide variety of emotions and someone "being emotional". The latter is almost always a pejorative, and there is a tendency to conflate that state with the former, which is simply the general human condition.
My twenty two cents, for what it's worth. Your turn.