If you are a kid who failed to get 4 GCSEs then one of two things has happened: you either aren't academically bright enough to be doing a BTEC in Business Studies or you spent too much time dicking about at school.
The fact he ended up getting expelled means we know it's the latter. He still sat his exams and by your own admission the expulsion was only a couple of weeks before the exams.
Its therefore fair to conclusion that him being expelled wasn't just because of this one incident but because it was part of a pattern of behaviour and that was the final straw. Otherwise he should have been able to have a fair crack at those exams and had every chance of still being able to get higher marks. Those few last couple of weeks missed would likely have been mainly revision not core teaching anyway. I don't think you can actually blame the expelling for his low marks. I think you have to stop being in denial about this and realise it's because he couldn't be arsed with school generally.
It doesn't really matter now about how you got here and who is to blame because he still has to now deal with the consequences of that.
The problem is that he demonstrated that his behaviour wasn't mature enough for school and if it's not mature enough for school, he probably isn't going to mature enough to do a BTEC.
He's ultimately ended up on a shit course because he can't prove he's good enough for the BTEC. This applies to his behaviour as much as his academic ability. His behaviour isn't just about him it's also about how it impacts on others and how much time staff have for dealing with bullshit. They don't want disruptive kids affecting kids who want to work. He is saying he is bored by the course he's on but actually I'd also have to put it out there that I would put money on the fact that he would have said the same about school too - he just doesn't like classroom work. The fact it's not challenging enough for him, is again kinda suggesting he wasn't working at school because he couldn't be arsed.
With that in mind, I really do question whether a BTEC in Business Studies is the right choice for him full stop. He can complain he's not allowed to do it but his attitude doesn't suggest that even if he was allowed to do it, he'd not get on with it anyway. Nor has he demonstrated really that he's ready to get his head down and get on with things. It's suggesting it's any old excuse not to do things he can't be arsed with and blaming everyone and everything else but his own attitude.
If he really wants to get on the BTEC course he needs to demonstrate that he's really changed, he really wants to do that course and he really is prepared to put the work it. He needs to show a massive change in attitude. A college usually will let someone switch courses if they can demonstrate this kind of commitment. So he needs to start asking questions about how he could go about doing this and planning for that. That may include doing something he doesn't want to do for a couple of years and then doing a night school class so he CAN get onto that course.
Or doing something completely differently.
The point is he is now learning that dicking about means you are going to have to do shit you don't want to and it may mean you need to find an alternative route because youve fucked up and the traditional way isn't for you. It's not life over - it is needing a massive kick up your own arse and focusing on what you want to achieve. And stop blaming everyone else for it. It's taking responsibility and proving yourself and proving that you've changed.
Some kids just don't suit institutions. I think his dismissal of apprenticeships is dumb and once again is proving his bad attitude. This doesn't necessarily mean he's lazy - he's proved his not from his side hustle - it means he lacks maturity and think he can opt out of doing things he can't be arsed with.
That does suggest to me that he is going to have to find his own way to make his side hustle his thing - part of this might mean (once again) knuckling down at a night school to get side qualifications for that.
The real danger he is he's just seeing this as an opt out of doing anything due to a bad attitude cos it's something he doesn't want to do more than anything else. Plenty of smart kids and kids from good family do this. It does sound like he needs one gigantic rocket up his arse from his parents about how he can't do everything in life he wants and just op out of thinks he can't be bothered with though. Otherwise you will end up with a whinging sofa loafer.
This kid is clearly not stupid but I do think you also need a change of attitude and to stop blaming the old school for where he is now because even if they were in the wrong feeding that narrative isn't going to help. The mentality you need to foster is one of determination and resilience to prove the school were wrong and that he can get his head down and do things he doesn't want to if the end goal is something he really wants.
This is 100% an attitude thing and your attitude matters here. Stop making excuses for him. Start saying you need to get your head out your arse and work twice as hard to make up for it. If you believe in him then you know he can do this and you need to get him to believe this and buy into that idea. Positive stuff looking forward and taking responsibility not negative shit looking back and blaming everyone. You need to lead that and say that part of your life has gone, stop holding on to it. Who are you now and wtf are you going to do about it. What CAN you do instead of wallowing in this life is unfair stuff.
It's not an easy place to be in. Some kids don't rise to that challenge and end up in a permanent rut. Other kids find that determination to go forward and actually change. You influence that heavily and yes you do have some tough things to admit here which might be hard to listen to. You have to though otherwise you fall into a cycle of self pity and life not being fair.
Life isn't fair. He needs to grow up and deal with it and turn it round.
Look forward not back.