It’s a Mormon University. I can understand kicking him out if they do not believe his conduct was honorable and in keeping with what they find acceptable. Yet, if he did the work and deserves to graduate then that should not be withheld from him.
In order to attend BYU you are required to sign the honor code. If you break the honor code, you can be expelled. To my understanding, this is very similar to what the Air Force Academy, as well as the other military academies do. To meet the graduation requirements of BYU you have to live according to the honor code while you are a student there and complete the required courses. He failed to fulfill both of the requirements for graduation and therefore did not earn his diploma.
I agree with the school’s right to exclude who they want and govern their students’ conduct, but this student might have a breach of contract claim. He met all the requirements to graduate, and lots of non-Mormons attend and graduate.