You are not logged in as the database owner or system administrator. You will not be able to save changes to tables that you do not own.

In Microsoft^® SQL Server™, each database has a database owner (dbo). The dbo is the creator of the database and has system administrator privileges inside the database. It is the dbo who determines the access and capabilities provided to other users.

If you are not the dbo, you will still be able to create diagrams showing any tables that you have permissions to see, however you won’t be able to perform all edits. Certain edits require SQL Server CREATE TABLE permission.

For more information, see Working in a Multi-User Environment.