oomis: “m’avreir” is a fan in Hebrew, you mean “mavir” igniting. But there is a significant difference between lighting a fire and extinguishing it, which is clearly the source of your confusion.
PM, you might be correct about the fan, though I cannot at this moment verify it. However, you may be unaware that “m’av-reir” is a transitive verb which means, “to create a spark.” It is not from the same shoresh as the word “avir” which means wind, which is the source for the Hebrew word for “wind machine” or fan. It is a different word. Ma-avir does NOT mean igniting. L’ha-avir means to move something from one place to another and has absoultely nothing to do with fire, unless you are committing the action of being ma-avir the flame from the pilot to the burner, or from a candle to a cigarette, etc. So ma’avir (not mavir, by the way, there is a patach under the mem and a chataf patach under the ayin)) means one who is moving something from one place to another. I hope this clears up the source of your confusion. And to say this for the final (I hope) time, when using a stove top or oven that has a CONTINUOUSLY LIT pilot (it NEVER EVER GOES OUT, unless you were to douse it with water or blow it out on purpose), it is NOT being extinguished when the burner is shut. The pilot remains LIT. The flame has simply been moved, and that is totally permissible on yom tov when cooking because it dos NOT EXINGUISH THE FLAME. Not even a little bit.