A common mistake I see people make that can ultimately lead to a horse becoming cinchy is tying their horses when they saddle them. Whenever you tie a horse up, you take away his ability to move his feet or flee from danger. Then, if he gets scared or reactive, in his mind the only thing he can do to escape is to pull back and try to break free from the halter and lead rope. The extra pressure of being tied and getting cinched up can overwhelm more sensitive horses. If you tie up a cinchy or young green-broke horse when saddling, if he spooks or the saddle slips under his belly, you’re going to have a big problem where not only could the horse potentially hurt himself, but now getting saddled will become a major source of fear.
If you have a cinchy horse, saddle him out in an open area like a roundpen. That way he doesn’t feel trapped, and if he wants to move his feet, he can. Always set your horse up for success, not failure.