People are different. I think that's the first thing. I get something of your essence by what you say so I contour my answer here to fit that. Now I posted elsewhere on THINQon about controlling one's anger and if you read that you'll see I was able to respond to a situation with a strategy that resolved it with minimal damage. Involved in that was a pretty tight control over my emotions; I wound them up or down as need be. But that said it wasn't done entirely out of cold calculation - one does follow the feeling to some extent (at least I do) and one directs it. Now a calculation about whether one's response is going to have good or bad consequences is another thing; that would depend on what one wants in the relationship or a bigger picture that surrounds it.
I do find it generally true that if one is totally authentic about one's meaning then things are simpler for oneself and others understand one better and even respect one. You can be respected even if it is all feeling and not entirely rational. You do have that feeling after all. So you were furious. I would suggest that you step aside from that fury, think about why it made you furious and then consider a way to express it, to make your point without dumping a truckload so to speak, because you are right - if you scream or introduce other baggage it will likely make matters worse.
So you want to address it directly. I assume you're not trying to change the other person - you can't really do that, they have to do that. All you can do is point it out, what made you mad. Do that by being absolutely clear and authentic. Say exactly how it made you feel and why. That can never be ignored and is absolutely riveting if done in the right way. It is not done by email, text or phone call but face to face. The other ways are impersonal and permit ambiguity which you don't want - it reduces authenticity. When what affected you is conveyed clearly together with all the reasons for it, then your job is done. It is the expression that is the job, nothing else. No strategy there. So you don't start to think "oh I won't express this" because "it won't work". That's not what it's about.
Not everyone does that in life. But I think it is important to do it. One doesn't "know" or "should know" or "assume". We never have another person's meaning alone and such communication is needed. You may need to practice doing it. Not in front of a mirror - because that results in a contrived affect later when what you want is a feedback that's not you looking at yourself. So practice with another person.
You learn the art by experience of yourself having a go and watching others do it. There is no substitute for experience. For most, they try to control their anger to use the strategy actually. What I described doing within myself is highly unusual. It is part of an art but not everyone can do it. Message me if you need more information there. It is of importance to realise that by being angry you give that other person power over you to determine your feelings. Is that something you care to accept?
Now it's possible some are upset by my returning to THINQon. If so, I encourage communication. I saw that Harvey left and that was unnecessary. Life is tough enough as it is for some people without alienating or excluding them. I once refused to help a friend, out of principle, of concern for his safety but I didn't stay in touch and later found he has most likely died. That is a knowledge I cannot lose and that is the danger we all face when we exclude people.
One last thought: Break a dish if you have to but they do cost to replace unfortunately :-) If you provide further details, a more precise answer for your situation can be furnished either by me or others on here who are prepared to care.