I agree with what you said. Moreover, I think mentioning CBT is relevant, because CBT teaches you what emotions are and what to do with them. CBT claims that cognitions (beliefs, thoughts, attitudes, assumptions etc) determine emotions, feelings and moods. E.g. if you think that you've lost something invaluable, you'll feel sad. If you think you were treated unfairly by others or the world, you'll feel angry. If you think that others or the world is supposed to be or do something, but doesn't, you'll feel frustrated.

Some feelings are more powerful and destructive than others. If you feel guilt, shame, anger, frustration, inferiority or depression for days, months, years, your life becomes endless pain. What's use of living in agony, if this can't help anyone? Even more, what if this feeling is a result of an irrational (incorrect or meaningless) belief to begin with?

On the other hand, once you already feel certain way, there's no use in scolding yourself for that, because it's counter-productive. So what if you realize that your feeling is a result of irrational belief? What do you mean you're not “supposed” to feel that way? By cursing yourself you'll only feel more guilt and self-hate. You have to accept yourself as who you are with whatever feelings you ever had or have.

It's ok to feel certain way. Certainly trying to quench feelings at all costs is irrational. But there are signs that feelings can be destructive and make you worse off. And getting rid of feelings that incapacitate you (like depression, anxiety or uncontrollable anger) is not always easy, sometimes you need a whole system. CBT might help you (I recommend reading David Burns's Feeling Good). According to CBT, cognitions determine your emotions and behavior, and behavior reinforces certain cognitions, so your task is to change your cognitions from irrational to more realistic, and sometimes change your behavior too.

On the other hand, feelings are not facts. If you feel angry, it doesn't mean that somebody indeed treated you unfairly. Anger is the result of thinking somebody or something is unfair, not evidence for it. People make a fallacy of using their own feelings as evidence, which David Burns calls emotional reasoning, one of the cognitive distortions.