Am I being unfair...GCSE results

[Abloodybigholeintheground]

Real first world problem here.....

My son has just got his GCSE results. He has been privately educated and the past year has been a complete battle-us/his teachers vs my son! He is a bright kid-not super genius but more than capable of achieving top grades. He is also bright enough to have worked out what he needed to do through the year to get by-keep out of trouble (mostly) but do no more.
He didn't work particularly for his exams-he did a bit but was kidding himself most of the time.
We set a bench mark for continuing at private school for sixth form-all grade B's or above. Although he isn't overly bothered about school per say he does have a good crowd of mates and loves the sports available to him which are not offered at the other sixth forms.
So-he did OK but got one C.
I think we should stick to our guns and pull him out-his stinking teenage attitude also weighs heavy in favour of this in my mind!
OH is going to bottle it-I am sure. He went to private school-in fact this school-and has a habit of not sticking to deals.
Should I stick to my guns and insist he leaves private education? He knew about this all along and didn't seem bothered (until last week when As came out and started to be nervous). It is only one grade-but what lesson does it teach him that he didn't achieve what was required but got to stay anyway?
Or am I being a miserable cow....

Just to add-all B's were more than achievable for him. He was told he could achieve A*/A in all bar one subject-ironically he got an A in that one!!

My DS is bright but monumentally lazy he did absolutely nothing and for his IGCSE's in his final report at the end of year 11 (post exams) was predicted B's for some subjects but achieved all A*'s.
We talked about it, he said he couldn't make himself work hard, I made it very clear that if that is the case I wasnt funding two more years at school he could go to our local state 6th form college and do nothing. We even looked at it so that he could see exactly what that meant. He agreed to work harder.
Two years later his report at the end of year 13 again predicted B's due to lack of industry not ability, he didn't even turn up for revision sessions; he got 2A*s and an A achieving 100% in maths! Frankly pleased as we were it just demonstrated that he can effortlessly wing things I suspect eventually he won't be able to.
OP I really feel your frustration it's really exasperating but I do know from experience you cannot make them work.
Many find A levels more work my DS did and also a big jump from GCSE's my DS didn't.