One who hates his own image

This body-image death spiral ends at universal self-hatred

"Up to one in five cosmetic surgery patients could suffer from body dysmorphic disorder" – again, the definition is sloppy. Body dysmorphic disorder is the irrational hatred of your body. You could easily argue that everybody having cosmetic surgery for reasons other than physical comfort has body dysmorphic disorder, just because it's irrational to hate yourself so much that you'd ask anyone to slice into you. Or you could argue that hating yourself that much is a maladaptive but understandable response to the pressures of your cultural environment.

Source: The Guardian

Body Dysmorphic Disorder (BDD)

But people who have body dysmorphic disorder (BDD) think about their real or perceived flaws for hours each day.

They can't control their negative thoughts and don't believe people who tell them that they look fine. Their thoughts may cause severe emotional distress and interfere with their daily functioning. They may miss work or school, avoid social situations and isolate themselves, even from family and friends, because they fear others will notice their flaws.

They may even undergo unnecessary plastic surgeries to correct perceived imperfections, never finding satisfaction with the results.

Source: ADAA (Anxiety and Depression Association of America)

Eisoptrophobia is the psychological condition of loathing to see one's own image, to see oneself in the mirror. Incidentally, this is distinct from spectrophobia, which is the fear of mirrors.

No need to get clinical about this answer. We have a perfectly good agent noun, 'self-hater', formed from 'self-hatred' (= 'self-hate'):

self-hatred n.
Hatred of oneself, esp. of one's actual self when contrasted with one's imagined self.

["self-ˈhatred, n.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/175271 (accessed January 08, 2016).]

As the "esp." highlights, the hatred may be of an actual self contrasted with an imagined self. So, 'self-hater' works well in the OP's example:

He always said he hated mirrors and I had assumed he was a self-hater, so I was shocked when I saw him apparently admiring his face in the glass!

It should be stipulated, however, that what the subject of the example saw in the "glass" might've been something considerably stronger and more admirable than himself.