I don't think we can really use killing sprees as an indication of anything at all in this context. If we consider it in the home schooling context, then we will have to also address the problem of the killing sprees in public schools in the US that have become so common, the schools are forced to have actual security guards patrolling their campuses and require students to wear photo ID while on the school campus at all times.

Also, of the parents whose children are being schooled because of learning disabilities, those children would have poor social skills regardless of where they were schooled. That just comes with the territory of having learning disabilities, but that problem is made much worse by the school systems. That's why the majority of young people in reform schools have learning disabilities. The schools are really messing them up.