I think part of it is not so much coddling, but just being adults. Kids are able to be molded; they are balls of potential that can go in a lot of directions and need a lot of work to live up to it. Adults are already in their mold. For the most part they know what they want from riding, and will work at a pace acceptable to them to get there. No one wants someone making demands at them, and I think an adult is more likely to back away from riding (or from a certain instructor)that orders them to work hard or says "do it again, and do it right" too often.
That's a good point, Laura. Kids are probably more accustomed to taking orders, for lack of a better term, from teachers/parents/authority figures. And maybe it's more natural for instructors to be more authoritative over kids than adult riders who are the same age or older than they are.
I taught lessons to 4-12 year olds throughout highschool and when I went away to college I began teaching lessons to my peers there. I have found that the college students are much more reserved and tentative about riding. I have also found that they have much more of an intuitive idea of when something feels right. So, when I see them struggling, I ask them if they want to do it again. This helps them gauge how they are doing. Little kids could go around doing something inherently wrong but they don't necessarily feel it. That is why I tell them to try something again. I also think that kids don't always realize how dangerous horses can be, whereas adults are aware of how scary riding can be.