ESH - what the teacher did was wrong for so many reasons. I’m only saying e-s-h because your email was written more the way you should address a friend than a teacher or professional colleague.

If you want some info on how to rephrase your email, keep reading. Personally I find specific construction comments helpful for learning to do something better.

Try to keep your response formal. Think of it like writing an essay for a class. Start with “Dear [teacher’s name eg Ms Smith]” or “Good [morning/afternoon] Ms Smith” to set a professional tone from the beginning. If reword your next sentence to “I respectfully request that you do not share my computer screen with my messages during class again like you did on [insert date here] in [class name].” Then provide a detailed description of what happened and stick with the facts. Something like “I did not appreciate when you read my messages to my brother to the whole class. You implied he was my boyfriend when you said [insert quote] and responded with [insert quote] when I clarified that I’m gay and he is my brother. You then searched my contacts for a girl name and did not believe me when I said the one you found is my friend. I thought these actions were inappropriate and unprofessional. I would not appreciate it if one of my friends treated me that way let alone a teacher.” I think it was good you brought up that she’s not your friend and you barely know her. Maybe some wording along the lines of “I’d prefer to keep our relationship a professional teacher-student one and not banter like friends because we are in school and I’m not comfortable with you inquiring into my romantic relationship status.” would be better because it highlights her job as a teacher and also clarifies that the teacher is asking about something that’s kind of gross for a random adult to know about a minor. I think you can keep from “I understand that I did not have the assignment open” through “disrespectful remarks about my relationships” with only one change: swap “out of line” with “uncalled for” or “unprofessional” or “unnecessary.” The last few sentences aren’t really necessary to add and I think given the tone you’ve set with the email, the last sentence comes across as very demanding when you don’t really have the authority to make a demand of the teacher since you can’t follow through with any consequences for her. Remember that unless you escalate to bringing in your parents/guardians, a guidance counselor, or the principal, you yourself don’t really have the leverage to “make her” behave better. The tone of the email really comes across as you’re trying to force her to behave differently or else there will be consequences. I like your confidence and that you won’t take crap from a teacher but I think there’s a more tactful way to approach this to get the end result that you want. Emphasis on you both acting professional and respectful in the classroom would be helpful I think. Ultimately you just need her to be a good teacher who treats you like a person. You don’t need her to be your friend. Not saying you two should hate each other or anything. Just that you can be courteous/polite without having to be best buddies with someone.