When I say "social structure" I mean the idea that people should feel compelled to follow societal norms. Even though school bullies don't enforce the same norms as society at large, they do enforce the norms of their peer group.

Conservatives (not all, but many) consider the principal that social convention be backed by actual violence, to be sufficiently important that establishing it at young age is worth some suffering or unfairness.

I think the idea here is that the system is self-reinforcing. An initially undifferentiated mix of children self-segregates as the children begin to perceive difference, and privileged/norm-conformant children persecute unprivileged/norm-nonconformant children. The persecution has the function of excluding the unlucky children from the social opportunities that come from access to privileged society (both because they are actively blocked by the other children, and because they block themselves by not realising they can seek opportunities or not considering themselves capable or worthwhile). This exclusion compounds as the cohort ages, rapidly becoming total. The result is that only a small selection of the cohort has access to privileged channels of society, maintaining a relatively low degree of competition at that level.