In the specific case of sickness, children are not expected to be responsible while sick. Kids are more fragile than parents and have less of a need to be doing things. As a kid, you can get away with staying home from school whenever you have the sniffles because you can easily make it up, and school will run just fine without you. As an adult, if you have a child that child will not be able to make it through the day easily if you take a sick day and just lay in bed all day. If you have a job usually calling out leaves consequences, even in something as seemingly simple as a fast-food job. These are the kinds of responsibilities that adults have that children lack. If it was possible to just stop the world when an adult got sick, surely it would be done, but it can't. Besides, as an adult you should be mature enough to not need to be babied for your sickness tbh.
In general, children are fragile and easily influenced. In addition, they're not responsible enough to be able to communicate often how sick they are; like Scarf said, they're not a good judge of their own sickness. I have a specific memory of getting a dangerously high fever and fighting my mom tooth and nail when she wanted to put me into a cold bath because I thought I was fine. Children are also more easily hurt than adults, because of their immaturity. As a child, you tend to think that the world revolves around you, and when the illusion is broken and the child realizes that they're not the most important thing in the world they're massively hurt. It's just the way kids are; it takes time to learn to think about things other than yourself and they just haven't had enough time yet. Adults, on the other hand, are expected to have some level of maturity that allows them to be treated as equal human beings and not as a lesser life form that needs protection and guidance, like children.
It's arguable whether children are treated better than adults though. I could easily argue that while children get coddled, they're also controlled in most aspects of life because of their youth and having parents setting the rules. I feel like as a young adult I'm currently being treated the best out of all age groups; when I want to, I can take the role of an adult and be treated like one, but when I'm around my parents I can revert to being a child and let my mother take care of me, buy food, etc. without infringing on my independence too much.
