I would like to take a stab at your scientific or “where are you getting your facts from” questions with my “in a nut shell” explanation:
Mental Illness affects the brain, which is a PHYSICAL ORGAN, therefore mental illness is BOTH a MENTAL/PHYSICAL illness. Here is a simple article that explains it for you.
To address your questions as to why he described his illness the way he did:
From experience, I think it is best to address difficult topics that are stigmatized from an emotional angle rather than scientific. People who are experiencing a similar life journey, regardless of the topic, will empathize and have compassion to an emotional tone. If he wanted to write a scientific paper, he would have prefaced this and cited sources.