"you're always told not to cross-control"
This should not be what you're taught. You should fly in coordinated flight, and that can often mean being cross-controlled.
Two very common examples of coordinated, cross-controlled flight are left hand turns on take off and steep turns.
Because of p-factor, on departure, you will have some amount of right pedal in, but to turn left (particularly in a nosewheel airplane), you need left aileron while you still have right pedal in, and its not unusual for full-power climbing left turns to have left aileron and right pedal in coordinated flight. You'll see this more in a high-performance airplane.
The second example is steep turns. After you roll into a steep turn to the left, say, the over-banking tendency will require right aileron with left pedal to keep the plane from increasing bank angle, in coordinated flight. The over-banking tendency is less pronounced below 45 degrees of bank in low aspect-ratio aircraft, like your typical Cessna.
So the rule is not "don't cross-control," but rather "fly coordinated"
That being said, the easiest way to get a plane into a spin is full cross control, and pull back on the stick. That's probably why you're taught never to do it.