She was, officially, his student at the time of the relationship. He admits this. He is trying to argue that, while he was officially her advisor at the time,

She was, officially, his student at the time of the relationship. He admits this. He is trying to argue that, while he was officially her advisor at the time, she had already completed all of the requirements of the degree, and he was only nominally her advisor as a result of academic technicalities.