There are different ways to overcome fears of doing backlflips depending on what you are afraid of.
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-Start with your arms by your ears with your palms towards the ceiling and your fingers pointing backward
-have your feet wider than hip width when you are learning (the wider they are the easier it is)
-slowly bend your knees and lean your knees over your toes
-slowly lean backward into the bridge keeping your arms by your ears
-look toward the ground
well there are a few ways you can get over that fear, you can think positive and say to yourself 'I'm not going to get hurt' or 'they wouldn't let me do this unless it was safe'. if you have a mat beneath you you most likely won't get hurt anyway and you can't do it until you try.
don't think of it just do it..... if the capability of you getting hurt is high they wont let you do it..... I'm sure you can do it....just don't think about it.
To overcome the fear, you should practice back handsprings on a trampoline, since it shouldn't hurt if you ever miss. Then practice back flips on the trampoline. Eventually, you'll develop more confidence and won't be as scared to flip backwards. When you're comfortable (and certain that you can do it on land), practice back handsprings on land. After you've mastered back handsprings (on land), practice jumping higher, so you could end up doing back flips instead without needing your hands.
There's nothing better than practice to get over your fears. Practice on a trampoline or a wedge mat. Remember that the worst thing that could happen is that you bump your head. But if you're on a spring floor it wont hurt.
NOTE: A back bend is a gymnastic skill that should only be done on mats with supervision of a qualified coach