There are many things they don’t want you to know but I also want to point out that not just narcissists are this way but everyone has their own ways or things they don’t want to be known about themselves by others. But since this is your question, here is my answer:
That they don’t want you to know they don’t care about you or your needs, boundaries, feelings, dreams etc and they will go the extra mile to make you think they do.
They don’t want you to know you are not the only one they are having sex with.
They don’t want you to know that today they idealize you but soon you will be history, only thought of or contacted when they need you again one day.
They don’t want you to know who they are, the real them is hidden quite well to most people.
They don’t want you to know they hate themselves.
They don’t want you to know they are using you.
They don’t want you to know they are lying to you much of the time.
They don’t want you to know that the gift they gave you wasn’t bought with money, sometimes it was stolen or bought for another but they took it back from them or if it was, if fact, bought in a store they don’t want you to know the real price unless it was quite costly, they will tell you it was 100x more than it actually was.
They don’t want you to know they are watching your every move, asking you as many questions as they can so they can be used against you one day soon or that the reason they want to get to know you friends and family is to one day turn them all against you so that you have noone left but them, in your eyes.
They don’t want to know everything they do is for a reason that will benefit them at the time at a later time.
They don't want you to know they enjoy seeing you sad because doing so makes them feel better.
They don’t want you to know who they text or talk to or are on messenger etc with. They don't want you to see their phone.
They don’t want you know how much they really hate you and can't stand your happiness. They don't want you to be happy because they aren't.
They don’t want you to know the trauma they went through that made them become who they are in order to be able to cope with every day life.
They don’t want you to know anything, they want you to solely depend on them and give them every single bit of your attention.
They don’t want you to know you are being played or manipulated, that the whole relationship is a game full of mind fucks or gas lighting to make you think you are crazy.
They don’t want you to know how much they need others or how they feel inside, they need constant admiration so will be the center of attention and look like they are having a blast doing so when in reality it is taking everything they got to fake how happy they are.
They don’t want you to know the real them. To be exposed is a big fear and if you threaten that you will be very sorry, I never recommend calling out a narcissist in front of others or even in private.
As I said, this is not just about narcissists, it’s about everyone in the world, we tend to target those with personality disorders but everyone has issues, if you don’t, please let me know and I will apologize but noone is perfect, noone is able to say they are the perfect partner or whatnot. I am borderline and high in narcissistic traits, I don’t ever intend to hurt anyone and I don’t want to be hurt. One of those two things is inevitable so I tend to do the first to avoid the second of the two. I just want to protect my fragile ego I very hesitantly admit.