Cakes, you said that people who want to do away with compulsory resits are denying the chance for children like yours to get GCSEs when they just need longer to do them and need to catch up.
NOBODY is advocating for a system where there are no chances of resits, where children only get one shot at it at a particular age.
What people want is the end to COMPULSORY resits, for children who are - for whatever reason - not in a position to take advantage of it that year. Some children are capable of resitting and improving their grade. I've known children who were close the first time, and with an extra year of input, to fill in some of the gaps, and who passed the next time. The smaller class and motivation they got from being in college made a difference. Others were totally turned off maths, hated it, wouldn't work, didn't attend. Others were cooperative but really just couldn't be bothered, and didn't put anything like enough effort in. Others were dyslexic or dyscalculic, and really wanted to be doing higher level courses, but simply weren't able to access the maths/English GCSE that they needed to get in. Insisting that all those children stay doing re-sits instead of something more productive, is what people are objecting to. Not refusing to give those who would like to carry on with maths and are capable, just needing more time, the opportunity.
You seem to think that there is some magic 'technique' that teachers can use in early secondary to catch all these low attainers up, and that they're just willfully not doing it, despite the fact that many teachers have told you that we've put best efforts in to teach in as many possible ways as we can, and some children still aren't catching up. It's not that we don't want to teach them the material, but some of them just aren't getting it, or aren't ready (or don't care!). No matter WHAT teaching techniques we use. If you seriously have better ideas of how to get them to understand the work, then DO that. Publish the methods, start a tutoring business, spread the word.
Of course not all sets get taught the same material. I have year 10s who are still working on place value. Why teach them calculus at that stage? They won't understand it, and it takes teaching and practice time away from things like place value - which not only will be more useful to them in a practical way, but if they actually really do understand it, will serve as a foundation for them to go on with maths at later stage if they wanted to. I have had too many children forced to rote learn techniques for passing exams (using formula triangles or 'finger tricks' or some other memory tip) that they have no clue what it's about, and forget immediately. It's a performing trick to do it on the exam. I don't want to teach like that either. I'd rather teach them what they understand, and give them skills that they can progress from.
Sets are crude measures, of course. Not everyone can have a perfectly individualised curriculum, and there might be someone in a lower set who could have done certain topics at a bit more depth in a higher set, and misses out as a result. Or people are held back by the number of places in a classroom. It's not perfect. But that's partly what you get with an education system that teaches 30 children in a class.
Flightpaths are not things that restrict children. They are rough measures to determine if a child is not achieving what you might expect based on previous scores. No-one just leaves a child on their flightpath and says 'well there you go then'. If a child isn't achieving what might be expected of them, they will be noticed and given more help. If a child seem to be able to do better than the flightpath predicts, they will be encouraged and supported and given all possible help to do this - schools and teachers love when a child outstrips the statistical expectations. It is hugely to the school's benefit, as well as the child's! If there is any chance that the child can catch-up and show extra progress beyond the statistical predication, the school will support this and try to make this happen. They want the best results from every child. The flightpath is simply a way the government has of marking the school. It does not limit the school's ambitions for a child.
Obviously, there are terrible schools out there and you must have had some awful experiences. But this doesn't mean that most schools are like that!
Teachers genuinely want children to do well. They want the freedom to actually teach, rather than force children through exams that aren't suitable. They want to take children from where they are when they come to them, and have them leave with more. They want children to learn useful maths or English skills, that will help them in the workplace, as well as allow them to go on to study the things that the child shows talent in. Right now, there are all sorts of barriers to that - children who aren't able to pass the exams being forced to do resits instead of the higher courses in other subjects that they're capable of. Students who find exams difficult, but could show the knowledge in other ways, still have to do endless resits. Students who find the GCSE exams difficulty, but still have to do them, instead of other, perfectly good numeracy qualifications, because someone has decided that GCSE is the only acceptable one. Students who are forced to do harder GCSE exams in the first place, when they need time to consolidate basic information and could be doing a lower tier of GCSE that allows them to demonstrate their skills. Many teachers want a 3-level GCSE , many want a separate numeracy qualification. This doesn't mean that they don't want to teach those who aren't able to do the higher qualification - quite the opposite. They'd rather people learned the lower stuff thoroughly first, were allowed to leave if that was all they wanted to do, or allowed to progress if they then wanted to do higher levels.