Why does the same flight take longer in one direction?
Mainly the jet stream — a band of very fast, high-altitude wind that aircraft fly with or against depending on direction.
What the jet stream is. Narrow currents of air circling the planet at roughly 9–12km altitude, which is precisely where airliners cruise. They form where warm and cold air masses meet, driven by temperature contrast and the Earth's rotation. In the northern hemisphere they generally flow west to east, and can reach 200–400 km/h, occasionally more.
The consequence. A flight from New York to London flies with the jet stream and gains ground speed. The return flies against it and loses ground speed. The difference commonly amounts to an hour or more on a transatlantic crossing, and the effect is strongest in winter when the temperature contrast driving the jet is greatest.
The aircraft's speed through the air is unchanged. What changes is its speed over the ground, which is what determines journey time.
Why airlines plan around it. Flight planning systems compute routes daily to ride favourable winds and avoid headwinds, which is why the track across the Atlantic changes day to day — the North Atlantic Tracks are republished twice daily for exactly this reason. Fuel loading, and occasionally whether a route is viable non-stop at all, depend on it.
Other contributors to directional asymmetry:
Air traffic routing and airspace restrictions differ by direction.
Departure and arrival procedures vary — a runway configuration or holding pattern can add time consistently at one end.
Scheduled block times are padded differently, and airlines build in buffer according to expected congestion at each airport and time of day.
The Coriolis effect does not directly cause this — the Earth's rotation carries the atmosphere with it, so an aircraft is not left behind by a spinning planet. Its role is indirect, in shaping the wind patterns themselves.