The Earth spins once per day.
Which means that if you live at the Equator,
The surface of the Earth with you on it,
is moving around a thousand miles per hour to the East,
relative to the centre of the Earth.
Even at 45º latitude,
the Earth's surface is moving 700 miles per hour to the East.
So it kinda seems like it should be faster for airplanes to fly west.
I mean, their destination is literally spinning towards them.
At the same time however, they are spinning away from their destination.
When we say the earth is going 1000 mph to the east,
that means that the ground, and airplanes on the ground, and even the air above the ground are all also moving 1000 mph to the east.
For an airplane to get anywhere, it has to start moving relative to the ground and through the air
at something like 100 or so mph.
So when it flies east, it's actually moving 1000 plus 100 mph to the east,
and when it flies west, it's actually moving 1000 minus 100 mph, to the east.
Yes, to go west you go east, just slower than the Earth is going east.
Unless you're within ten or so miles of the poles, in which case a brisk westward walk will take you legitimately west.
That said, planes do often take different amounts of time to fly the same route in different directions,
because of winds in the upper atmosphere like the jetstream that they either have at their tail, or have to fly into.
The prevailing direction of these winds is largely caused by the Coriolis effect,
which is caused by the fact that different parts of the Earth are moving east at different speeds, which happens because the Earth is round and spinning.
So, airplane travel times are influenced by the rotation of the Earth, just not in a straightforward way.