Wind is the main element contributing to the stability of an airplane. Aircraft require lift to remain airborne, lift generated by wind passing over the wings. The shape of a wing is such that the upper surface is longer then the bottom surface. As the wing passes through the air it flows over the top side creating lower air pressure causing the wing to lift.
When aircraft are positioned for takeoff, they try to head into the wind. This acts like a jumpstart as the amount of wind naturally generated passing under the wing makes it that much easier for the engine to create enough thrust to increase the speed of air passing over the wing to the point creating takeoff.
Taking off directly into the wind allows for the plane to progress forward without adding the drag of corrections required to overcome the effect of offside or cross winds that may be trying to pull the plane off course.
Taking off in a mild steady crosswind, though not a desirable situation, is usually more manageable then landing in a crosswind. As you clear the ground, once you are a few hundred feet up, if the plane is slid sideways a bit it’s of no matter, as long as forward airspeed is maintained.
Landing is a completely different situation. When approaching the runway at the low altitude needed for landing crosswinds can ruin your whole day.
Generally each airplane is rated for the amount of crosswind it can withstand and still land safely. Large commercial jets being able to withstand a greater crosswind then small two passenger aircraft.
The weight and bulk of a large airliner would require a pretty hefty gust of wind to disrupt it’s direction of flight. Not to say they aren’t dangerous, but a minor puff of wind isn’t going to knock these planes out of the air.
Small aircraft can easily weigh less then 1,000 lbs. With this light weight plane, that can glide seemingly forever in the event of engine failure at altitude, a unexpected crosswind gust of 5mph can send the unaccustomed pilot off course enough to miss the runway altogether.
Sliding 150′ off to one side may not make much difference on the takeoff of a commercial airliner at a large international airport. For a small plane landing at a rural airport it can mean the difference between a black top or concreted landing surface and a stand of pine trees reaching 50′ into the air, just as your about to touch down.
Landing leaves very little time or airspace to compensate for unexpected events. If radio communications are available current weather conditions should always be monitored. A wind sock, (required at all airports) is in view, a reasonable indication of wind conditions and direction can be obtained.
No matter what, if your uncomfortable with current wind conditions go find a different airport to land at. If your still on the ground with unstable crosswind conditions just stay there. Cross winds can ruin your whole day, always think conservative when it comes to deciding whether or not to fly your airplane.