????? mavir is the verb you are looking for than means to ignite a fire and is forbidden on Yom Tov. It is used numerous times in Chumash, for example in Pashas Mishpatim ??? ???? ?????? ?? ????? However none of this is relevant the issue at hand of turning off the fire.
You didn’t read what I wrote. The problem is not that you are extinguishing the pilot flame, you are NOT, as you pointed out. The problem is that when you light the fire on the stove you have created a second larger flame on the burner and it is this flame that you are extinguishing, which is absolutely forbidden. If you would have looked at the sources I provided you would have seen that even making an existing flame smaller is forbidden on Yom Tov, except under specific circumstances”
I was taught the word was m’avreir, (and I never heard it in connection with a fan, but will concede that I could be mistaken about that, though I am certain the word used was m’avreir, as I would have no reason to make up such a word on my own, and did not know the word for fan), but still, mav-ir (to make something burn), and ma-avir (to move something from place to place) are clearly two different words. Now that this is a given, I still contend that turning off the burner is NOT extinguishing the flame, as I have been taught all my life, it is merely re-locating it. If it were extinguished, the pilot would go out (as used to happen in very old-fashioned stoves, some of which were also in my parents’ time),w here the pilot had to be re-lit each time the stove was turned on.