Because of the rotation of the earth, the wind tends to flow from west to east. So when you fly towards the east, the wind pushes the plane. When you fly from east to west, you are flying against the wind, which slows the plane down.
The prevailing wind in the upper atmosphere where airliners fly (the jet stream) flows west to east over the US, often at over 100 mph. So a plane with a maximum air speed of 500 mph might have a ground speed of 600 mph flying east but only 400 mph flying west. I suspect this holds true across the mid-latitudes worldwide, but I imagine that there may be latitudes where the opposite is true, perhaps near the equator. Also wind speeds and directions at low altitudes may not correspond to those higher up.
Your logic does not consider the resistance of the counter-force moving at 100MPH. A 100MPH current of water impedes movement of an object more than a 100MPH current of low-density, upper-atmosphere air.