Theresa May accused Jeremy Corbyn of seeking to "pull up the ladder" after taking advantage of a good education as her grammar school policy came under fire.
Labour leader Jeremy Corbyn warned school reforms desired by the Prime Minister were the sign of a Government "heading backwards to a failed segregation for the few and second-class schooling for the many".
Mrs May had sought to play on both her and Mr Corbyn's grammar school backgrounds, although Tory MPs appeared to be less vocal in their support during Prime Minister's Questions when compared to recent weeks due to concerns over the school proposals.
In exchanges dominated by grammar schools, Mrs May swerved questions from Mr Corbyn although insisted she wants them to provide opportunities for a wide range of pupils.
She added to Mr Corbyn: "There are many examples across the country of different ways in which that's done through selective education.
"But you talk about the good education for every child. That is exactly what our policy is about.
"There are 1.25 million children today who are in schools that are not good or outstanding. There are parents today that fear their children are not getting the good education to enable them to get on in life.
"I believe in the education that is right for every child. It is the Labour Party that has stifled opportunity, stifled ambition in this country.
"It is members of the Labour Party who will take the advantages of a good education for themselves and pull up the ladder behind them for other people."
Mr Corbyn replied: "It's not about pulling up ladders, it's about providing a ladder for every child."
Mr Corbyn also quoted former prime minister David Cameron, labelling him a critic of grammar schools, in support of his argument.
He told Mrs May: "Isn't (Mr Cameron) correct that what we need is investment in all of our schools, a good school for every child, not this selection at the age of 11?"
Mrs May repeated a good school is needed for every child.
In his final question, Mr Corbyn quoted criticism from Ofsted chief inspector Sir Michael Wilshaw.
The Labour leader noted Sir Michael described the idea that the poor will benefit from a return to grammar schools as "palpable tosh and nonsense".
Mr Corbyn went on: "Isn't all this proof that the Conservative Party's green paper addresses none of the actual crises facing our schools system - a real terms cut in school budgets, half a million pupils in super-size classes, a crisis in teacher recruitment and retention, a rising number of unqualified teachers in classrooms, vital teaching assistants losing their jobs?
"Isn't this the case of a Government heading backwards to a failed segregation for the few and second-class schooling for the many?
"Can't we do better than this?"
Mrs May claimed some of Mr Corbyn's facts were wrong, arguing there are more teachers than 2010 and fewer pupils in super-size classes.
She added to Mr Corbyn: "You have opposed every measure that we have introduced to improve the quality of education in this country.
"You have opposed measures that increase parental choice, that increase the freedom for headteachers to run their schools, you've opposed the opportunity for people to set up the free schools - these are all changes that are leading to improvements in our education system and we will build on those with our new policies."
Earlier in their exchanges, Mr Corbyn - who received loud cheers from his MPs as he pursued the issue - asked if Mrs May could name any experts who backed her policy.
He also pressed the PM if pupils at potential "feeder primary schools in poorer areas" will receive automatic places at grammar school.
But Mr Corbyn received no answers as Mrs May stuck to her line of the reforms offering "more opportunities" for children.
The PM also tried to take advantage of Mr Corbyn's grammar school background with little success.
She reminded Mr Corbyn: "You went to a grammar school, I went to a grammar school - it's what got us where we are today but my side might be rather happier about that than yours."
The Labour leader replied: "The two things the Prime Minister and I have in common is we can both remember the 1950s and we can both remember going to a grammar school.
"My point is simply this - every child should have the best possible education they can have.
"We don't need and never should divide children at the age of 11 - a life-changing decision where the majority end up losing out."
In her final words to Mr Corbyn during the session, Mrs May floated the idea that it could be her opposite number's final appearance at the despatch box.
Mr Corbyn will find out later this month if he has fended off the challenge of Owen Smith for the Labour leadership.
Mrs May said: "I accept that he and I don't agree on everything. Well, actually we probably don't agree on anything.
"But I must say to him he has made his mark.
"Let's just think of some of the things that the right honourable gentleman has introduced - he wants coal mines without mining them, submarines without sailing them and he wants to be Labour leader without leading them.
"One thing we know, whoever is Labour leader after their leadership election it'll be the country that loses."