Whilst home schooling can work, the outcomes for HE children are worse than for children in care in terms of results.
Can you tell me where this is from? Is this at 16, or later in life? Is this based on GCSE results? (which are prohibitively expensive for home educators and involve jumping through many hoops). I just wonder what outcomes are being measured here. Does this include all the children with extra needs whose hands are forced by the education system failing them? Does it include the children "off rolled" by schools because the school thinks their behaviour is too difficult or their results are going to be non existent? If so, this is bound to make schools look better and home education look worse.
I can only speak anecdotally, but I know of my DD's friends that many looked quite poor at 16 if all you measured it by was their GCSE results at that point in time compared to schools. The barriers to GCSEs mean that many home educators spread them out over a number of years, or only take the minimum needed for the next step, or take them at college.
Now they are all late teens and early twenties, they are looking a very successful bunch indeed. Many are at university, some are in jobs which they really enjoy and always aspired to do, some have started their own businesses and are doing extremely well for themselves. All have dreams, ambitions, goals, and all are making them happen.
My own DDs gained 9 and 10 GCSEs respectively, almost exclusively As and A*s. They may have gained one or two extra at school (not least because it cost a couple of thousand in exam fees alone for us to do as many as we did).. My youngest is currently at university doing a Masters in Physics. In school she hated science. She certainly wouldn't be where she is today without home ed.