You are confusing airspeed and groundspeed. Groundspeed is entirely irrelevant to an aeroplane except as far as navigation is concerned. It does not affect flight one iota.
Many non-pilots find this hard to grasp, especially model flyers, some of whom are convinced their model gains airspeed on turning into wind, and loses it turning downwind!
I used to take a chap in the back of the Chipmunk who swore he could tell when we had a tail wind by the increased blast of cold air coming in under the back of the canopy!