Offering of a grad class rescinded for incomprehensible reason A course came up that I was interested in (C*algebras). It's a grad class but was offered to a select group of undergrads including myself. I accepted the offer but then once the class started I received an email saying the following: 

"Dear XXX,

I have just noticed that you have not completed Math 311. I think it would be a terrible idea for you to be doing the operator algebra course before completing that. It would also be irresponsible of me to let you do it. This isn't really dependent on why you didn't complete the course. The appearance alone would make me look bad.

Best, XXX" 

I replied that I have 100% on all but one assignment and an A+ on the midterm. I haven't yet taken the final but it will be scheduled by the end of the semester. (I couldn't take the exam for health reasons that he knows of.)

He knows I am an A+ student and has given me 2 A+'s in the 2 classes I have taken with him. I tried speaking with the instructor of the Math 311 course and asked him to speak with said prof to see if he could convince him that I know the material but I'm not sure how that will go. 

I don't know why this prof would rescind the invitation when we seemed to have previously had a good rapport. The prof does know that this would be my 6th class for the term which may be a contributing factor. (4th at 4th year or above)    

Is there anything else I can do to increase my chance of getting into this class?

Also I don't want to damage my relationship with this prof further as I hoped to ask them to do a summer research project.
Look, the thing with these kinds of questions is that process varies significantly from institution to institution based on their regulations, bylaws, etc.  I actually agree with the instructor's decision, even though the email is unprofessional.  It is usually not allowed for a student to take a course in which they have not yet completed the prerequisite for that course.

Having said this, there may be a solution.  In many institutions, exceptions like these are handled by a specific entity such as the Faculty Council, the Department Council, the Vice-Dean for Undergraduate Studies, the Vice-Dean for Graduate Studies, the Faculty Dean, etc. Since I don't know your institution, I can't begin to say which one of these would be the proper route to take, but typically a request or a petition could be sent to the responsible body, and they would then study it and make a decision based on your unique circumstances. 

My advice in this situation would not be to get upset, nor to talk about how the reason was "incomprehensible" or anything along these lines.  I would say you that you should write a letter/email/petition to whomever is responsible in your faculty and ask that an exception can be made based on the circumstances and situation that you pointed out in your question.  Talking with the instructor of the Math 311 course probably won't help because technically, the professor of the Grad course is simply following proper university procedures and guidelines. if you are close with the instructor of the Grad course that you want to take and are familiar with him, I would say that you should talk to him in person, and ask him about what the official channels would be for getting this exception and see if he would support you in this. 

Don't attack. Don't accuse. Don't get upset. Just try to find out the solution that complies with all relevant bylaws and regulations.  That is my humble advice.