Never, ever, EVER tell an athlete you are going to spot them and then pull away! Safety first, last and always! If an athlete is not ready there has got to be a reason you have to address and deal with. Go back a step in the progressions, put them on a different surface, put a mat on the floor so they have to tumble higher but land on a softer surface, walk into the spot so that they have to trust you will be there instead of seeing you there the whole time (this is a mental release technique I use with some athletes and you have to be 100 percent sure of their skill ability and your ability to spot them if they bail to do it) motivate, encourage - but don't ever pull away from a spot.
If you do and they get hurt, technically and legally you are liable. Second they lose trust in you as a man/woman of your word even though all you are trying to do is show them they can do it. Then you fight that battle with every new skill they struggle with. Then as has been said others in the gym see it and automatically internalize that if you did it to Suzie you are going to do it to them as well.
My best strategies besides those I described above are these:
1.) I would rather have them do it 500 times safely than 1 time and be hurt. So I keep them on equipment, tumble track, rod floor, etc until they have done it so much (they don't count but I do) that they essentially tell me they have it.
2.) When they are about to do it by themselves I give them the scenarios, I describe what would be the most likely event if they mess up and even go through how that landing might be. Usually what they are freaking out about is landing on their head, neck, face, or flat on their back. Once they are sure that the worse thing may be landing on their toes pitching forward to hands, hands and knees etc. then they are usually ok with doing it. Now mind if they do what they have been trained to do without change they should land on their feet, but I keep it honest with them.
3.) Make sure that no matter what they do, keep all the lead up skills the same. Don't run faster, hard, extra, anything that will make it feel different than it has been. Do the same thing that they have been trained to do. If the lead up skills are the same (assuming they are correctly done) then there should not be an issue with the last "big trick" skill.
4.) Video and play back for them several times before they attempt it by themselves. Having them see themselves do the skill, even if with a spot is powerful reinforcement in their mind that they can actually do it.
5.) Don't let them end on a "bad" one. The last one of the day always has to be a good one or the best one. That is what they leave you with. Leave them with a positive mental picture of that skill/day and not a negative.