I dreaded trying to talk about this because I don't understand much of what draws me to it. So forgive me for not really addressing the film itself, as I've done so many times.
The thing is, I'm aware that this isn't necessarily the most popular choice when it comes to the Tarkovsky cannon. I also know that there might be a perfectly valid reason for this, not necessarily because THE MIRROR isn't great (it most certainly is).
My theory is simple. By the time I saw my first Tarkovsky in 2008, my art cinema experience was fairly limited (some Bergman, Godard, two Malick's, Fellini, Herzog, Lynch). I first saw RUBLEV, then SOLARIS, then IVAN'S CHILDHOOD, and finally STALKER. Each of these is undoubtedly great, probably greater than my pick. But each of these films taught me how to comprehend his cinema. The great sculptor of time requires more patience and a rewiring of the brain that becomes so attached to traditional storytelling techniques. This much is obvious.
John, our resident Tarkovsky expert, will undoubtedly articulate his appeal and his truth. I can't. Partly because none of these films are fresh in my mind. I saw THE MIRROR in 2013, right after a miserable experience at a book fair, where I consequently saw John, my infant son dangling impatiently from my chest. I can't recall much, frankly. But I do remember immediately thinking, "this is one of the best movies I've ever seen." Good enough for me.
PS, I'm eager to check out STALKER (completed after two very sleepy attempts), ANDREI RUBLEV (pissed me off bc of a very disturbing real horse killing), and SOLARIS (watched at work with John, aka very distracting). THE MIRROR and IVAN'S CHILDHOOD were watched undeterred.