It's possible to observe critically the reality described below without criticizing individual parents for their behavior. While I think in most places people who are paranoid about "child abduction" are a bit off, I get that people respond to social pressure and attempt to conform to social norms. If no one else is walking to school, you're going to be less likely to let your kid walk, etc. If your neighborhood has no sidewalks, or if the "close" school is across a theoretically but not really traverseable 8 lane road it might not really be wise for kids to walk.
I guess there are two issues here. One is parental attitudes about appropriate levels of supervision and concerns about certain safety issues. The other is how we build our neighborhoods.