Question

Why is friction important to a gymnast working on a set of parallel bars

Answer 1

friction is important for a gymnast while working on a set of bars to maintain its grip or else if friction won't be there so he may get a sever injury

Answer 2

Gravity , which is always trying to bring any object to the ground that is having a potential energy will also bring the gymnast down as he has potential while working in the parallel bars.
The only 2 forces that would help him bee up is the air resistance ( which is negligible ) and the friction.

Friction helps a resisting force that is created between the legs and rods to keep the person up.
 If he takes out his leg then there would be only air resistance which would not help the person stay up.
Hence friction plays an important role in the gymnast working with parallel bars.