Speaking as an NRA Instructor for the last 21 years, the number one reason is safety and control of the situation. For a kid it's too easy to get lively with the muzzle and the trigger and send rounds everywhere without regard for safety. Especially kids raised on video games and modern media. 10 rds from a 10/22 will go sizzling downrange in less than 2 seconds and once fired those rounds can't be recalled no matter how much you may want that. Reason #2 is to make certain shooter technique is correct. With a bolt in recoil and those tiny movements going on, it's more difficult to analyze technique like grip, trigger control, breathing and follow through. Marksmen are born of necessity. Having only one shot available makes you better. Having 10 shots engenders the spray and pray mentality, mostly because it's so much fun! But fun doesn't breed competence. I use a single shot bolt action to start children out on and move to a Single Action Ruger Super Single Six when it is time to move onto handguns from rifles. Same principles apply for the handgun but more so.
Just for the record, technique, safety, and other firearm skills were taught to my kids years ago on the BB gun.
It is not the same, but it was the teaching platform we started on. Living in Suburbia, it was something we could do often in the back yard. It allowed them to demonstrate safe handling prior to the first firearm.