A: Well, I guess you will have to accept the fact that you may be boring LOL ;).
But seriously, this behavior is very common and pretty much all bettas do in deed do that. You asked if they are yawning: The answer is no. (don't be relieved just yet, it still doesn't prove that you are not boring after all LOL). I believe that the reason bettas do that is because of their labyrinth.
It is believed that because Bettas originally came from shallow stagnant waters, which contained little oxygen, Bettas had to adapt by developing a new organ, called a “Labyrinth”, which would allow them to get the oxygen they need to survive directly from the atmosphere, above the water’s surface.
The “Labyrinth” is an accessory respiratory organ, located in the gill chamber alongside and above the normal gills. It is composed of bony plates covered by a membrane through which flows venous blood. By gaseous exchange, passing through the labyrinth organ, the oxygen content is passed immediately into the blood stream, then the used air is expelled. Because only small amounts of air can be stored into the labyrinth, bettas must make frequent trips to the surface to replenish it. This is why you will see your betta regularly going back up to the surface of his bowl to take a gulp of air.
The labyrinth allows betta to survive in oxygen deprived environments, such as small bowls, and to also survive outside of water for what seems a long period of time. Bettas are sometimes found on the floor, having jumped out of their bowl, and after lying on the carpet for quite sometime, come right back to life when returned to their water. The labyrinth also allows us, breeders, to ship bettas in small amounts of water (just enough to cover their bodies) without suffering fatalities.
As you see, bettas are very special fish. Now in what way might the opening of a betta's mouth and gills for a second be beneficial to the labyrinth? I am not exactly sure. Perhaps it is a way for them to flush out something. Another thought that comes to mind is that bettas are bubble nesters and that maybe this "yawning" behavior may have something to do with this as well. If you have seen a betta blow a bubble nest you would notice that the mouth movements are very similar to that of the "yawning".
Boys: Rosewell and Ren
Girls: Juno, Circe, Iris, Rhea