It may sound improbable, but thanks to Michael Gove, the knives are out for the independent sector again. We are, apparently, unfairly good. It is “morally indefensible”, he said a couple of weeks ago, that so many people who achieve success in so many different walks of life have been to independent schools.

Well, it is not morally indefensible. That is just lazy rhetoric. It is certainly a stark fact. But we should try to understand it better before jumping to simplistic conclusions.

Why are independent schools successful? For they certainly are; Gove was right about that bit. But if we are not careful, this is where the simplistic conclusions begin to stack up.

Is it because independent schools have more money? Not so. The average spend per pupil in the independent sector is not higher than in the maintained sector, once you factor in all the administrative and capital costs of running a school. Certainly, some independent schools are able to spend highly, but most are not. Annual fees in most independent schools outside London are actually lower than university tuition fees (and they cover a great deal more). We do not have more money, but perhaps we spend it better.

Or is it because independent schools are viciously selective? Once again, not so. A few independent schools - especially those in London and other big cities - are able to select their pupils. Most of the others are hardly selective at all.

Or is it because independent schools cater only to the affluent middle class? Not so, again. Over the past 15 years, independent schools have expanded their intake dramatically. The latest Independent Schools Council census reveals that 33 per cent of students are on some form of fee assistance, and that proportion is growing. The level of means-tested assistance rose by almost 10 per cent in Headmasters’ and Headmistresses’ Conference schools in the past year alone. The spread of ethnicity is striking, too. It is no surprise that the most successful independent schools also show the highest proportions of free places and of assistance with fees.

Or is it that independent schools are just pleasureless exam factories? Clearly not so. The breadth of success that Gove quotes is proof against that. Independent schools believe, above all, in variety and in balanced and rounded education. Perhaps we do well because we recognise the needs of individual students.

Or is it all down to the “old boy network”? Absolutely not so. Most independent schools - and there are hundreds across the UK - are not especially well known. Because of the lazy rhetoric about social inclusion, independent school students are not favoured in their applications to universities or to employers. Increasingly, the reverse.

So why are independent schools so successful? It is because we have two huge advantages. The first is that all of our students, and all of their families, believe that education is genuinely and hugely important. They all believe that a good education can transform lives. So we have a level of support - personal, emotional and intellectual - that is vital to us, our teachers and our students.

And the other mystery ingredient? It is our independence, which means we decide the ethos and values of our schools. We design our own curricula and we plan our own co-curricular lives. We employ and reward and develop our own teachers. We work with our own students to deliver the education that best suits them. We raise our own money and we choose how that money is spent. We take responsibility for our own leadership. It is not easy or comfortable, but it is worth it.

So is that morally indefensible? No, it is not. Surely it is morally indefensible that so many successive governments have hobbled state schools by denying them the freedoms, advantages, challenges and opportunities that independent schools relish. Gove understands that well - just look at his academies programme.

Independent schools are not the problem. The principles that underpin the best independent education are actually a big part of the solution. His policies, if not his rhetoric, suggest that Gove has grasped that.

Kenneth Durham is headmaster of University College School, London, and chairman of the Headmasters’ and Headmistresses’ Conference.