I have no particular comment on home educating, but I can back up what another poster in regards to CBT for autistic people.
I tried CBT as a teen due to depression and anxiety, and it only made me feel worse. I felt condescended to, and like they were trying to trick me into getting better by getting me to come up with coping strategies I'd already tried and found unsuccessful. I dropped out of CBT after a few months and waited years before trying therapy again; after that first experience, I just didn't trust that it would actually help. Eventually I tried DBT, and then moved on to a mixed-approach counsellor combining techniques from talk therapy, DBT, relational therapy, transactional analysis, trauma therapy, and more. I've now been with that counsellor for several years and consider my current sessions to be "maintenance" more than active treatment, and it's done wonders for my wellbeing.
Not all CBT is ineffective for autistic people, and not all autistic people find CBT ineffective, but that does seem to be a common theme. I know some therapists provide an adapted form of CBT with autism in mind, but me and many of my autistic friends have found DBT much more effective. I won't go into why I find it better than CBT so as not to turn this into more of an essay than it already is. It's worth looking into DBT providers and trauma therapy* providers with a specific interest or specialism in working with autistic patients. The National Autistic Society resources may come in handy when looking into what's best for your DS. You're clearly keen to help and support him, and having that solid parental advocacy in his corner is already a great start.
*This is not to say that homeschooling is inherently traumatic, but an acknowledgement of current theories that many autistic people seem to be "easily traumatised." That's an oversimplification, I know, but some studies suggest that autistic people develop trauma responses to "non-traumatic" events. In my experience keeping that in mind when approaching therapy has been incredibly helpful, and may explain why he feels homeschooling has exacerbated his issues. Please understand that I'm not suggesting that you traumatised your DS with homeschool, just that this isn't an abnormal response in autistic people. Appropriate therapy will likely help him process this and understand that you made the best decision available to you at the time.