Hello OP.
I home ed 3 younger children. My eldest 2 are about to go into year 9 and year 12 at school. I am obviously pro home ed.
I just wanted to say that all the arguments for and against home ed could go on all night. The fact is that not all children who go to school receive an education. So the fact you are withdrawing him is not the biggest issue.
The bit that stands out in your posts is that your ds is unhappy. I think you are doing the right thing prioritising his mental health. Without that, he will not have a bright future at all. So for that reason alone, I think you are doing the right thing.
My eldest has done very well at school. School suits him and he will be staying on for A levels. School does not suit everyone and I hate this idea that without school you have no prospects.
My DH left school at the end of year 9, 20 years ago. He had undiagnosed dyslexia, anxiety and a pretty rough home life. He was labeled as a difficult, angry lazy young man. He spent a year hanging about, smoking weed and playing computer games.
When he was almost 16 he started an apprenticeship. From that day, he has worked 6 days a week, every week for the past 20 years. He is now a happily married father of 5 earning almost 50k a year.
True, he is not an educated man. He couldn't tell you about Shakespeare or Pythagoras. He has no interest in cell structure or logic gates. He just about manages to write sweet things in my birthday cards. But he is a happy, hard working successful man.
I think you should take your son out of the system that is clearly failing him. Let him take a breather and work out what it is that he wants from his life. Encourage him to look at vocational courses. Encourage him to read and learn something just for the sake of learning. Let him discover the joy of learning again. When he finds it I bet there will be no stopping him.
Of course, if he has his heart set on being a doctor or a vet, then he will probably be disappointed, but if he has other ideas there are all sorts of ways of getting there. Why don't you go and talk to some colleges that offer courses for 14-16 year olds and see if anything appeals to him.
Good luck to you and your son.