If you haven't had him for a while it is normal as he was exposed to other bettas without a sense of his lien territory. There is nothing to mark in the cup as his territory so yeah. My guy was one of those display ones so he had a fake plant and marmio ball to claim, he was flaring a lot in the store and that is one reason why I got him. He instantly flares when a mirror is put in front of him. I also do the fight training just to keep him fit by putting a choostick on the glass and he chases, and flares at it. I would put him through more training but one, I don't fight bettas and never will, and I have no space to setup an area for a really good technique to make him a better swimmer. Sounds like I fight huh? Just to remind you I have never fought bettas...
Just keep the mirror there for a while, you can set it against a tank wall for a while, he may start to get more territorial. Some never do, but having him flare will help him stretch his fins.