Firstly, and I cannot over emphasise this, don't write angry. It is too easy in the age of email communication to say things that you probably wouldn't say if you had 24 hours to calm down, and the benefit of a printed copy of your correspondence to read before you hit send. As a solicitor who spends a lot of time watching what people do when they are angry trust me, you are not your best self. Calm down, if you can't calm down, have someone who will be honest with you read your draft.
Actually, just get someone else to look at it
If the letter is important you should really have someone else look at it. I have always said that a big part of my job as a lawyer is actually quite simple, that is I am not personally involved in the matter. I have a different perspective because it is not my life, or my money, or my feelings. Now I am also a professional advocate, but often a different person who is not connected to the problem can read the letter and give you a different perspective.
Your letter may not say what you think it says because of assumed knowledge, or it may not be interpreted by a third party (your friend, or the person you are writing to) in the way that it sounded in your mind. Get your friend to read it and if they have no feedback for you, then ask them to tell you what they think the letter is about.
Wait a day
There are very few items of written correspondence that need to be sent now, today, this minute. Even emails rarely require an immediate response. Most of the letters or emails you will write can actually wait until tomorrow. Draft a response now but then print out the draft, put it aside, and come back and read it tomorrow. You might think of something important overnight that you should mention in your correspondence, or you might have a different approach with a bit of distance. You can use this time to ask a friend to look at it (see the above point).
Check spelling and grammar
You will not be taken seriously if you have spelling and grammatical errors in your letter. This probably isn't a case of educational prejudice, but rather the letter will not appear to be well consider or well thought out if there are errors (because that implies that you didn't read it through before sending it). We get all types of important documents here, job applications, court documents or letters of offer with spelling or grammar mistakes and it is generally (along with other things) and indicator that it was not a well prepared or thought out document.
On a Board I am on I recently received a letter from an educated woman with clear errors, and I said either she has not written this letter herself someone else did on her behalf, or she was so incensed when she read the letter that I wouldn't worry too much about the accusations there in. In the end once that person had calmed down and someone spoke to them face to face, they couldn't provide details to back up any of the accusations in their letter.
Don't try and use 'legal' words
You are who you are, don't try and be something else. We often see people without any legal training trying to use legal words, it rarely works, it normally weakens their argument. They usually use the words in a fashion that, while technically accurate, is not the correct way to use that word. It is not the lack of legal degree that undoes the person it is the incorrect use or over use of 'legal' words. The same would no doubt apply for medical terminology, political terminology or anything else you can Google. Don't over use language you aren't familiar with in an attempt to sound more intelligent, it almost always backfires.
You are entitled to your opinion, and you are entitled to be heard, you don't have to use certain language. Use your own voice.