OP I think home education is not the right path for you or your child. You need to bat this back to your local authority and badger them for better provision for your child - either through EOTAS, a referral to a special needs school or unit or to hire a 1-1 support in a mainstream school setting. There are groups on Facebook that will help you with this I think searching Not Fine In School maybe a good starting point.
Despite all the vitriol you have thrown at the HE community, we still try to offer help and support and have empathy for your situation.
However, I do think you need recognise that home education means we take on the full financial burden of educating our children. There are no financial incentives, no grants, loans, benefits etc that are paid to us to home educate. Plus any exams, qualifications etc have to be paid for in full by us, not the local authorities or department of education. Therefore to verbally attack many of us who struggle financially to educate our children is unfair.
Finally, you do not have to be a teacher, tutor, etc to home educate, but it would probably surprise you how many teachers, lecturers and other professionals home educate, often side by side with a diverse group of families who have educating their children outside a state school setting as a priority.
On a side note: I personally don’t ‘teach’ Black History Month in a group setting, however my child has access to a diverse educational setting, using tutors from the all over the globe for certain topics. We also cover world history, religions and cultures on a regular basis, throughout the year. There are plenty of BHM resources online, but rather than dedicate just a few weeks a year (as some schools do) diversity is part of our everyday educational philosophy and practice.