The problem is both their home lives and mixing them with the general population of students. Diverting funds from public schools that refuse to remove violent or anti-social students to intensive programs that can correct their behavior puts pressure on them to do just that. You address a bad home situation by giving them a safe space during the day at a specialized school that can focus on behavioral problems, and in extreme cases, by removing them from abusive or neglectful homes.

Let me know if you need additional explanation. I advocated for this combination elsewhere in this thread multiple times already. It's not really that confusing. It's pretty simple.