Why do American parents hover instead of teaching their kids that 'might makes right' and letting them figure out how to solve all of their own problems including bullies?

Because might does NOT make right.

As a teacher and parent, I've seen my fair share of bullies.  A first grader stands no chance against the third grade bully.  Without adult intervention, the child could be severely injured in that "kids stuff."  The psychological toll is equally if not more devastating.

Just because we intervene for safety, doesn't mean we don't also teach appropriate social skills to both the bully and his/her target.

Well .. That is a hard question to answer because .. Not all American (or any demographic for that matter) 'Hover'.

Granted, "Hovering" parents don't allow their children to learn and grow as individuals and members of society .. THEY tend to take care of every and all issues their child faces.  We ALL know that is counter productive.

I think most parents agree that guiding their children, and providing them with resources to help them deal with social aspects of living in modern society is a healthy way to raise their children. Children need to learn to think on their own, and handle situations that arise .. They need to learn what their options are .. Because THAT is how they metamorphasize into responsible and mature adults.