If Earth rotates, why doesn't it affect the airplane’s distance?
Why doesn’t the earth’s rotation affect the distance between two points on the earth? Because distance is distance. The distance from Tokyo to New York is a physical measurement and it doesn’t change, no matter whether the earth is rotating in one direction or the other, or not even rotating at all.
Let’s continue the thought. Why doesn’t flying west to east or east to west take more time than the other? After all, shouldn’t the earth’s rotation be moving faster under the aircraft in one direction than the other direction?
In other words, if the earth is rotating, why doesn’t an airplane traveling from Paris to New York take less time than traveling from New York to Paris? After all, the Earth is rotating such that the earth should be moving faster under an aircraft that is flying toward the west.
The answer is that the atmosphere that the aircraft is flying within is rotating with the earth. In a broad sense, the Earth and the atmosphere can be thought of as a single integral system.
Distance as opposed to Time
However, there is a nuance to that answer. Because of the Earth’s rotation, the atmosphere and anything (like an airplane) operating within it is subject to certain physical forces. One is known as the Coriolis Effect or Coriolis Force.
Definition: an effect whereby a mass moving in a rotating system experiences a force (the Coriolis force ) acting perpendicular to the direction of motion and to the axis of rotation. On the earth, the effect tends to deflect moving objects to the right in the northern hemisphere and to the left in the southern and is important in the formation of cyclonic weather systems.
As a result, the Coriolis Effect causes the prevailing winds in different parts of the globe to have broad differing natural flows as opposed to local wind currents or local weather pattern-related flows.
These wind patterns can have significant effects on aircraft ground speeds. That implies that depending upon the aircraft’s direction of flight, there is a potential for significantly longer times to fly between two cities.
So you see, that while the earth’s rotation doesn’t have any effect on the distance an airplane flies, because of the prevailing winds it absolutely can affect the time an aircraft takes to fly between two points on the Earth’s surface.
EDIT:
Based upon what I believe is a flawed Comment in response to the original answer, I’ve chosen to expand on some of the different types of localized winds. As my answer states, the mass of the earth’s atmosphere as does, in fact rotate with the earth. And as I stated the atmosphere is also affected by the Coriolis Effect.
But there are a number of other semi-widespread or more localized atmospheric influences that cause airflows (winds) to vary direction, tumble, etc..
Some of them are:
Wind flows around obstructions like mountains, buildings, etc. are often turbulent and even change direction. In fact, the stronger the wind, the more it’s likely to be turbulent.
Wind flows around High and Low pressure systems. Winds flow clockwise around a High pressure system that is north of the equator and counterclockwise around one south of the equator. For Low pressure systems the flows are opposite; counterclockwise around Highs north of the equator and clockwise around those south of the equator.
The sun heating the surface of the earth causes the heated atmosphere to rise and that creates airflows toward the rising air.
Similarly, beaches and coastlines are subject to onshore and off shore wind flows based upon temperature differences during the day and night.
Again, relating to heated air, clouds with vertical development like cumulus and cumulonimbus (thunderstorms) clouds will usually cause surface wind flows toward the buildup, and in the case of thunderstorms Gust Fronts — strong outward flowing gust fronts are not uncommon.
Hurricanes and tornados are both created by and create strong winds.