This is because your theme is not checking the comment status of posts in the correct way. You may like to point your theme’s author to what they are doing wrong, and how to fix it.

The plugin tries its very best to hide this (and any other comment-related) messages.

If you still see the message, then it means your theme is overriding this behaviour, and you will have to edit its files manually to remove it. Two common approaches are to either delete or comment out the relevant lines in wp-content/your-theme/comments.php, or to add a declaration to wp-content/your-theme/style.css that hides the message from your visitors. In either case, make sure you know what you are doing!

Don’t install this plugin!

Go to the edit page for the post you want to disable comments on. Scroll down to the “Discussion” box, where you will find the comment options for that post. If you don’t see a “Discussion” box, then click on “Screen Options” at the top of your screen, and make sure the “Discussion” checkbox is checked.

You can also bulk-edit the comment status of multiple posts from the posts screen.

Go to the tools page for the Disable Comments plugin and utilize the Delete Comments tool to delete all comments or according to the specified post types from your database.