"I'm sorry, but Junior is freaking out and gets performance anxiety" - So your solution is to let Junior learn that fears win out as opposed to facing a challenge and overcoming it.
"I'm sorry, but she's really nervous and I just don't think it's good for her" - Then don't have her or him in a competitive sport, play an instrument, pariticpate in dance..etc, etc......where they'lll inevitably have to perform in front of others.
I could use numerous other examples.
Too many parents are bailing their children out when it comes time to facing a fear or a challenge. It's OK for your kids to feel this way. Most people get nervous, scared, anxious before a game, a dance, a recital, a performance or whatever it is. It's PART of the process. It's PART of growing up. When you bail them out because your kids "freaks out" you're laying the ground work for them to do it over and over again....and have thus enabled them and taught them an awful life lesson...or lack thereof you just taught them.
No wonder kids are getting softer and softer. It's sad.