Assuming anonymous's premises
(1) intelligent people are more likely to end up in high paid jobs, and
(ii) intelligence is partly inherited (genetic)
He (I assume a "he" - don't know why) concludes that the children of the higher paid are more likely to be intelligent, on average. That's true, other things being equal.
However, anonymous then goes on to claim this shows kids of working class people are less intelligent on average. That does not follow. The conclusion certainly isn't "unavoidable", as anon claimed.
If 2 groups A and B (e.g. black and white, working class and middle class, gays and straights, whatever) make a up the population, but group A members are largely or wholly prevented from competing effectively for intelligent, higher paid jobs because of non-genetic factors, then yes, those in such jobs will be more intelligent on average than the members of either group A or B on average.
However there's clearly no reason as yet to suppose that, as the children of group A don't show up much in those jobs, the children of group B are, on average, more intelligent than those of group A.
Moreover, and this is the amusing bit, if there's no independent, prior reason for supposing the members of group B are genetically more intelligent than group A on average, we can also conclude those in group B who are not in intelligent jobs will then be LESS intelligent on average than those in group A.
So, assuming no prior reason to suppose working class people are innately less intelligent, anonymous's premises should lead us to suppose that, other things being equal, those middle class people not in intelligent jobs will be less intelligent on average than working class people. This is because they have actually been weeded out on the basis of lower intelligence, whereas the members of group A - the working classes - largely have not.
So, knowing what we do about the way non-genetic factors prevent both black and working class people from competing effectively for the intelligent jobs, we should conclude that the children of middle class people/white people not in intelligent higher paid jobs will be LESS intelligent than those of working class people/black people, on average.
This would account for Tim, nice but dim, syndrome.
Yet Woodhead claims it's primarily lack of innate intelligence which explains why many kids are uninterested in his lessons, disruptive, etc. Actually, if it's lack of innate intelligence which supposedly produces such problem behaviour, it should actually be the kids of the middle-classes-not-in-intelligent-jobs whom Woodhead should be singling out.
Yet he just ignores the obvious non-genetic factors preventing working class kids from competing effectively for intelligent jobs, and jumps to the conclusion that the children of the working classes are less intelligent, on average.
That does say a lot about him, I'd suggest.