It wasn't my claim that home-schooled students have difficulty acquiring social skills in general, it was that they miss out on a specific set of social skills, namely dealing with people who are different from them, whom they do not like, who have different opinions, etc... while maintaining productivity. Basically: learning to work together with a diverse set of peers and maybe to empathize with people who see the world differently, or to at least gain experience in coping with differences.

The study/quote supports this by giving a rough indication of how most public schools are diverse places. Obviously, this doesn't "prove" the entirety of my statements, it just offers a small amount of support in the area of public schools being either segregated or diverse.