I flare my boys everyday, I've been doing it forever. It's a form of entertainment for them and me. A solitary, monotonous life isn't the best and some excitement now and then helps. In fact I've had 2 bettas bite their tails when not flared for a week. From total boredom. Flaring also helps stretch their fins and also helps relieve constipation in some cases. As long as it is not overdone, flaring is fine. As P3 said, your betta may have a neurotic issue. A single occurrence like that cannot be used to debunk what people have been doing for years now.
I don't use a mirror with my bettas (anymore) but that is only because I have moved them all so they are side by side in their tanks (with 3-4 inches between them). They flare on their own once or twice a day at each other for a few seconds... then it's over.
When I first got my VT his tail fin was dragging low and thin.. but now his tail stays spread out (not flaring spread, but holding it up and open) because he is now stronger doing so then he was when he was in the cup at the store.
They will flare at anything they deem fit to, and nothing you do will stop them. They will flare at you, at a shiny rock, their thermometer. It's just what they do.
It doesn't necessarily stress them out, but gets their energy levels up, adrenaline rush, etc. When they are done, most will be more active immediately following the flaring session and that isn't a bad thing.
If you wish not to make yours flare, that's fine. You may state it that you wish not to and why. But you don't want to give misinformation to new owners about it, especially when we recommend it as a way to beat boredom/tail biting.
Xander and I have flaring competitions together, he starts (and usually wins). I'd hate to think that he is hurting himself doing something he chooses and is natural for them. Luckily, it's not harming him ;)
you can't stop bettas from flaring. it's natural for them. some, do it at everything(Cup did, even sounds, and my mom's CT flares at my finger, the cat, or even my face). it strengthens their fins, stimulates blood flow to the fins(making them more colorful), and keeps them entertained...
IMO, flaring is actually good for them (already mentioned above). If you never flare them they become weak and their fins would clamp (specially long finned), and it affects their immune system too.
I flare mine between 15 - 60 minutes daily by lifting the divider about 2cm. Or replace the normal divider with one that has a small hole in the center. They won't constantly flare, only when they come across each others sight.
I still dont know if I should put the mirror so he flares or not...
You guys dont know what my betta does when he looks himself at the mirror, he starts to panic and move around his aquarium like a bullet, breathing SO HARD and showing his black beard and opening his fins to the point of almost stretching them.