Something I’ve found to help students when they’re learning to gybe is to separate the gybe from the act of turning the boat. A gybe can require no turning at all, and understanding this will improve your gybes and reduce your likelihood of capsizing.

Most of the time, the reason we are gybing is because we want to turn and go the other way while sailing downwind. Maybe we've reached Ashby Ave and we have to head back before we start to feel the disapproving glare of the day leader through their binoculars. Or we're doing tight circles around a buoy and have to keep turning through the gybe. But really, gybing has nothing to do with turning, other than if we're turning downwind, we have to eventually gybe or we just can't continue the turn.

The gybe itself is nothing more than changing tacks (from port to starboard or vice versa) while sailing downwind. Or to put it more simply: a gybe is flipping the sail from one side of the boat to the other. If you’re on a dead downwind run, there is no turning needed. In fact, there are reasons to gybe that don't involve a turn at all. A common case is during racing--if you're on a dead run and want to obtain right of way by switching from port to starboard tack. No turning needed. Or maybe you're headed back home and the wind shifts a bit and you realize you're now sailing by the lee, so you flip the sail to get yourself out of accidental gybe territory. No turning needed.

I've noticed a lot of students (understandably) connect the turn and the gybe and want to turn through the gybe, from broad reach to broad reach, which can often result in a capsize. To help disconnect the two actions I've started doing this exercise:

I've found this tends to create a light bulb moment and hopefully makes gybing in general a little smoother.