Why does this cancel a flight? Well first know that if the world is perfect, you'll come into land on a runway and the wind will be blowing straight against you. This means it's moving fast over your wings providing lift, even if the airplane isn't moving very fast along the ground. You've got time to think and control things and hit the ground at the angle you want.
Unfortunately runways are huge slabs of pavement on the ground that don't rotate, so when the wind changes, it complicates things. It doesn't take much wind at all to blow a little airplane off course. You can line up on the runway all you want but you will get pushed over and drift off.
So to account for this you tilt the wings into the wind. This means the air moving over them will pull you one direction, the wind is pushing you the other direction, and you fly straight. Remember... since the plane is moving forward, there's always more air moving over the wings than against them, so this effect of the air over the wings is a powerful thing that fixes most every problem. If you can get that air to pull the wings the right direction (mainly up, with a little bit of "over") you're golden.
You also kick the rudder the opposite way to keep the nose pointed forward. You can't land the airplane at a crab angle on the runway because it'll mess up the wheels and tires, plus you'll be rolling on the ground in a direction that would take you off the runway. Bad.
Getting these two things to happen at the same time, perfectly balanced and always changing second-to-second as the wind gusts change is why it took me so damn long to solo.
But I digress... picture an airplane with its wings tilted, you eventually see that it can only tilt so much, then you risk hitting a wingtip on the ground! Bad idea! So you fly into your little airport, try your landing, realize the wind is pushing you so far to one side that you can't keep the wingtip out of the way, and climb up again. Or maybe you can't add enough opposite rudder to keep the nose pointed straight. Either way, try another runway. Or another airport. Or you can do what we did... look at the weather as it is, realize the winds are already in the wrong direction, and call the whole thing off.
Even big airplanes have issues with crosswinds. It takes more to mess with them, sure, but they also have to account for the drift and direction control.