@John Mace: The jet stream article is good as far as it goes. But there’s a lot more to prevailing winds at altitude besides the jet stream itself.
Your first part is 100% right. Irrelevant, but right.
Your second part is 100% wrong. Not stupid, just wrong. But since you’re starting from a bad idea, the rest of your good thinking after that is going off in a silly direction. Let’s see if we can fix that. 
The Earth is rotating towards the East. But it’s all the Earth, not just part of it. The rocks, the oceans, *and *the air are all turning at the same rate: 24 hours per day. There is no sense in which the air is lagging behind the ocean which is lagging behind the rocks; they all rotate together. So that’s not where wind is coming from.
There are two large-scale sources of wind.
One is that it’s hotter at the equator than the poles. This creates a net wind from poles to equator at the surface and a net wind the other way at altitude. As the wind moves poleward or equator-ward the Coriolis force curves what would otherwise be a wind to north or south into a wind to the east or west. See Hadley cell - Wikipedia for more.
The other is that as the Earth rotates different areas switch between day and night. All else equal air is heated and wants to rise in the day and cools and wants to descend in the night. The edge of twilight moves around the world at about 1000mph at the equator and about 500 mph at the latitude of Europe or southern Canada. Which means the edge of daylight is moving much faster than the wind can move to catch up. But it tries.
Then we can add in all the rest of the things that affect weather, such as fronts, terrain, clouds, precipitation, etc. Wind, and especially wind at the surface, is the result of all those factors.
Here is a live realtime map of wind in the Americas and adjacent oceans https://earth.nullschool.net/ . As you can see, it’s pretty complicated. Far more complicated than a simple straight flow from west to east.
The long term average effect is that at the latitude of the USA, the wind generally flows from generally west to generally east. But not in a simple linear fashion. At jetliner altitudes the wind is generally 10ish percent of the speed of the airplane. So as between going with or against the wind, the total difference is about 20%. Or about 1 hour in a nominally 5 hour flight.