Is the instructor a super admin?  I know my instructors go into the course and pick their session and click on the people to get their list of attendees.

The instructor is a regular user assigned as instructor.
As such they are not enrolled in any sessions either.
 

Per the Instructor User Guide 
“To access the course in which you’re an instructor, log into your learning platform, then access your main menu and select the My Courses and Learning Plans. Find the course card on this page, then click on the course card to access the course’s main page. “  

I have seen instances where the instructor has multiple profiles, and the profile assigned to the course as the instructor was not the profile that the instructor was logged into.  Especially if they are not seeing it on their My courses list, the profile they are using is most likely not assigned as the instructor for the course. 

Alternatively, if you assign the instructor to the session, and the instructor happens to be logged into the system, they will probably need to log out and log back in again to see the course.  I have that happen as well. 

Thanks for the response Annarose, a couple of good suggestions there.

The user in question has only one profile.

I also managed to replicate the issue with a test user.

I created a test course with one session and an associated event then assigned the test user as instructor. The test user was unable to see the test course in their My Courses list at this point - (logout/cache-clear/login)

As soon as the test user was enrolled in a session, the card appeared and they were able to access all the instructor functionality.

I am entertaining a theory that if the user has access to the catalog that the course resides in when the Instructor role is granted, then the card will be visible to that user. I have some case testing ahead of me.

Weird!  I tested this on my side with a test instructor that did not have access to my test course from a catalog and made sure they were not enrolled.  That profile was able to access the course from their My Courses page.  I would open a support ticket and see if there is not some other advanced setting or bug that is keeping your instructor from seeing that course without enrolling them

Thanks Annarose, I will do just that. 

Cheers!