When the profile on Instagram is closed, then you can accept solution: allow the person to subscribe to you or not. If your the page is open to all, there is no such privilege: you can subscribe any.
So what about those who don’t need to see your publication?
How to unsubscribe an unnecessary user from yourself Instagram?
Like Twitter, in this case there is only one option – block a person. In this case, he will automatically unsubscribe from you, however, you will also stop following him.
To block a user (to unsubscribe from himself) go to his profile, click on the menu button in the form of three dots, and then click on “block”.
That’s all, an unnecessary person will no longer follow you, and You didn’t have to close your page.