It sounds as if you already told her you didn't want her to read your emails. Her response was that she has a right to read your personal communications.
You need to do a little bit of reading before you approach your mother again about this, and do it quickly. Read about boundaries, because it will be critical to having a healthy relationship with your mother. In fact, all healthy relationships need and respect boundaries.
Boundaries exist everywhere in the form of laws. You're not allowed to go into a stranger's house and leave with their TV. You're not allowed to leave the scene of an accident where someone has been injured. Laws are there for our protection, so that we can coexist safely and respectfully. There are consequences to breaking these legal boundaries. Personal boundaries function in much the same way.
People often say they set a boundary, but it didn’t help. There’s an art to setting boundaries. If it’s done in anger or by nagging, you won’t be heard. Boundaries are not meant to punish, but are for your well-being and protection. They’re more effective when you’re assertive, calm, firm, and courteous. If that doesn’t work, you may need to communicate consequences to encourage compliance. It’s essential, however, that you never threaten a consequence you’re not fully prepared to carry out.
Read about boundaries until you are sure you can not only set them but can explain why they are important. Your mother will push back. You need to remain calm and reiterate your boundary and why you're imposing one. Set a consequence and state it. Then walk the walk.
The conversation should take place when you're both in a good place mentally. It can go something like this (this example is truncated for brevity's sake):
You: Mom, I love you, and it's important to me that we have the best relationship we can have. (Add to this what you can: how grateful you are for all that she's done, etc.) But I want you to know that I'm hurt when you don't respect my requests for privacy. Therefore I've changed all my passwords on my accounts, and ask that you respect them.
Mom: But I'm you're mother. I have a right to know what's going on in your life!
You: You do know what's going on in my life to a great extent. You see what's going on and I tell you about things you don't see. But I'm an adult, and I am entitled to some privacy. That's why I've changed...
Mom: But (another reason, say...) I don't feel that you are respecting my rights as a mother if you...
You: Let's discuss your rights as a mother...... (discussion)
You: I agree that (what you do agree with). We'll talk about (bombshell issues) another time. But right now, I don't agree that you have a right to read my personal communications. I've given this a lot of thought and decided this was best for our relationship. Please respect that, and don't ask me for my passwords. I will not give them to you, and I will feel disrespected if you ask even though I've explained this to you.
What is a consequence? You refuse to talk about it.
You: Mom, you know how I feel about this. I love you, and I don't want to argue with you, so I'm not going to discuss this any more. If you keep on insisting, I'll have to (leave/hang up.)
If it continues, tell you you'll talk to her again (whenever), and hope you don't have this argument again.
Eventually she'll learn the boundary.
You don't have to move out to establish boundaries. You just have to believe you deserve certain privileges and be able to articulate them to people who are accustomed to treating you as if you don't.
Again, read more about boundaries. They will help you understand more about some causes of conflict in relationships and how to minimize what you can in healthy ways.
What Are Boundaries
Having a conversation to assert your boundaries