There's a distinction that sounds obvious until it actually has to be applied in real time: a feeling is not the same thing as a fact. Feeling scared doesn't mean something dangerous is actually happening. Feeling certain doesn't mean something is true. Feeling worthless doesn't make someone worthless. The emotion is real. What it's pointing at isn't always accurate.
Most people know this intellectually. Applying it in a moment of strong feeling is considerably harder, because strong feelings arrive with their own certainty. Emotions are experienced as information about reality, not as one perspective on it. That's what makes them so easy to reason from, and what makes it so costly when the feeling happens to be inaccurate.
The other problem
The opposite error is just as common: treating feelings as noise to be managed, ignored, or overridden by logic. The "I shouldn't feel this way" move. The intellectualizing that keeps the emotion at arm's length. The careful analysis that never quite touches what's actually happening underneath it.
This doesn't resolve anything. Unfelt feelings don't dissolve. They tend to show up in other places and in less legible forms. Both errors, treating emotion as fact and dismissing emotion as irrelevant, miss what feelings are actually for. They carry real information. They're just not always accurate reporters, and they need to be checked against what's actually true in the situation.
Wise mind
There's a concept in DBT called Wise Mind: the place where emotional experience and rational thinking actually meet. Not one overriding the other, but both being held at once. The emotional mind knows what something feels like and cares deeply about it. The rational mind can check whether the interpretation is accurate and think through what comes next. Wise Mind is what happens when both are given a seat.
It doesn't feel cool and measured. It often feels more like a slower kind of knowing, a sense of what's true that accounts for both what the feeling is saying and what the facts actually are. The anger is real and it's pointing at something real. The story the anger is telling isn't the whole picture. Both of those things can be true at the same time.
What it looks like in practice
Someone is furious after a difficult conversation. Emotional mind: this was deliberate, nothing is going to change, the relationship can't be trusted. Rational mind: this person has shown up reliably before, one conversation doesn't define a pattern, there's context being left out. Wise Mind: something real happened and it hurt, and the relationship isn't what the anger is making it feel like right now.
Getting there doesn't require suppressing the anger. It requires holding it alongside some other information long enough for a clearer picture to form. That's a skill. It builds with practice, and it makes a noticeable difference in how decisions get made and how relationships actually go.