My own favoured explanation is that the Left realized that its traditional appeal - focused on the abolition of serious material poverty (starvation, homelessness, exposure to life-threatening cold etc.) and equal opportunity according to merit rather than birth.
By the 1950s it was apparent that these had already happened - so the Left needed a new agenda, and started systematically lying about reality.
This was the 'turn' from Old Left to New Left - old Left being about prosperity and opportunity - New Left (which became Political Correctness) about favourable outcomes for designated victim groups, and about 'oppression' of these groups conceptualized as psychological suffering rather than life-threatening deprivation.
In Measuring the mind: education and psychology in England c1860-1990, Adrian Wooldridge puts forward his list of reasons why the New Left in Britain turned against psychometric testing, especially IQ testing - and the previously dominant meritocratic project (pages 322-4).
(These changes in the British socialist movement were initiated by ideas outlined in New Fabian Essays of 1952, edited by the egregious Richard Crossman. I'm pretty sure I read this book in a library copy in my mid teens - certainly I read The Future of Socialism by the equally egregious Anthony Crosland of 1956 - which was another literary launch pad for the British New Left.)
1. Disillusion with the 1945-51 Labour government, and a wish to distance the future Labour Party from their methods and policies. Having tasted the reality of Old Leftism - Implementation of the 1944 Butler education act, massive nationalization, creation of the National Health Service and the Welfare State - they discovered it didn't live up to their hopes and dreams, and the coming generation wanted something different.
At another point,Wooldridge emphasises the inappropriate way that IQ testing done on one particular day in a child's life (i.e. 'the eleven plus') was (literally terrifyingly) misused as a way of the state allocating specific individual children to different types of school.
Whereas the tests were originally intended as a way in which an academic school could detect talent among those from non-academic (lower class, rural) backgrounds and those whose formal education had been insufficient or ineffective from the perspective of specific subjects (like Latin and Mathematics). Public, Private or Grammar schools could use psychometric testing offer specific poor but bright children opportunities they would otherwise have lacked.
There is a world of difference between the privilege of being offered an opportunity, and the coercion of state allocation.
2. Anti-communism. This is interesting, because in that era meritocracy was associated with the Soviet Union! By rejecting meritocracy the Labour Party could burnish its (in some respects unconvincing) anti-Soviet credentials in the Cold War era.
3. Fear of betrayal.
The British Left is replete with legends of betrayal (Ramsay Macdonald, Oswald Mosley, 1926 TUC General Council, 1984 'scab' Nottingham miners etc...).
The brooding over betrayal functions as a focus for unifying and mobilizing people with hatred and resentment - in this instance the hatred of class traitors (who rose from the working class and 'forgot their roots') and resentment of those who took advantage of the equal opportunities (by means of scholarships) - and 'creamed off' the working class intelligentsia.
Also the supposed low self esteem of those who had failed - and failed not by being victims of class prejudice against them, but because they were not-good-enough in the free-for-all competition of the meritocracy. This was blamed on psychometric testing and all it represented.
4. Rejection of the Labour Party program to nationalize all possible institutions (known as Clause Four) - the New (moderate, Gaitskellite) socialism would instead be focused on a crusade against the supposed injustice of selectivity and stratification in education - with the notion that this would abolish class divisions and create a truly socialist society.
The idea was that if everybody from all classes went to the same schools and mixed freely, then Britain would cease to be the most 'class-ridden' country in the world (sic) and become more like the classless USA (sic).
Therefore selection must be got rid of, implying that the the psychometric instruments of selection should be discredited.
Well, all this may be so to some extent - it would not be a great surprise if something of this kind was contributory; but none of these four explanations account for the expansile dishonesty and sheer venom of the New Left in relation to the subject of innate and hereditary differences - especially between groups.
For this level of hostility there can be no good explanation - no plausible explanation in terms of being a by-product of the intention to do good; but rather a bad explanation - in terms of the Left becoming, from this point, ever more evil: ever more destructive of good.
A major indicator of this dishonesty is that the imprecision and defects of IQ testing when applied to specific individual children largely disappear when IQ testing is applied to groups - and yet it was group differences which the Left specifically ruled as taboo.
Dishonesty makes science impossible; but added to this in a lethal cocktail was gross incompetence in designing and interpreting research studies. And here I need to append a warning in relation to this very useful book.
Wooldridge does not remark on the astonishing incompetence of the critiques of psychometrics, perhaps because he does not understand the science of intelligence, nor does he make any apparent effort to do so.
Measuring the mind is well-worth reading - but (from a scientific perspective) it is no more than a deft and cleverly-constructed mosaic of other people's opinions harvested from a very wide range of reading and meticulously documented.
Whenever the author ventures anything like a scientific opinion (which isn't terribly often) it is clear that Wooldridge doesn't have a clue; although (being a typical Economist journalist in this respect) he deploys a writing style characterized by the assumption of omniscience.
This scientific incompetence enables Wooldridge to avoid potentially career-threatening hate-facts in relation to group differences and heredity. But in doing so, the book has been seriously distorted.
In sum, this book is very useful, and seems historically solid on topics like the history of party and academic politics, but it is unsound on the science of psychometrics itself; because the author is scientifically incompetent and evasively dishonest - neither of which is surprising nor even particularly blameworthy, but these things need to be said lest readers be misled by the brilliant style and encyclopedic coverage.
All of which is to say that this book is social and political history written by an historian of the modern kind; it is not a work in the genre of the history of ideas.