The head of Oxford University has rejected calls from the government to sponsor schools.
Louise Richardson says Oxford was “very good” as a university, but had “no experience” of running schools.
The call for universities to help set up schools was part of the proposals to expand grammar schools.
But Prof Richardson said to become involved in the government’s plans for changing schools would be a “distraction from our core mission”.
The government’s Green Paper on grammar schools proposes that universities should have to either sponsor a school or help set up a new school – otherwise they would not be able to charge higher tuition fees.
About 60 universities, including Birmingham and King’s College London, already sponsor or support schools – and the government argues that the expertise of universities should be harnessed to improve schools and drive social mobility.
But Oxford vice-chancellor Prof Richardson said that her university should focus on what it knew best, which was delivering higher education.
Oxford was named as the best in the world in global rankings published on Wednesday.
“We’re very good at running a university. But we have no experience of running schools, so I think it would be a distraction,” said Prof Richardson.
“We’re deeply sympathetic to the idea of social mobility through education – and we have extensive relationships with schools.”
But she said it was “insulting” to head teachers and school leaders to think that universities could step in and do a better job of running schools.
The university revealed earlier this year that it would be admitting the highest proportion of state school students for at least 40 years.
This followed spending of £6m per year on outreach projects with schools, encouraging state school pupils to apply.
But Prof Richardson said that such work was separate from running a school and that the university should not take on activities that would “distract our time, energy and resources”.
The Oxford vice-chancellor also argued for the importance of free speech and for allowing university students to hear views they might find “objectionable”.
And she said she opposed both the government’s Prevent anti-extremism strategy and students who wanted to have “safe spaces”, where views they found offensive would not be allowed, on campus.
A Department for Education spokeswoman said: “There are already some excellent examples of universities sponsoring schools – they have expertise that can really help improve our education system, and it’s in their own interests to improve attainment in schools.
“With 1.25 million children in underperforming schools, we have put forward new proposals, asking how our world-leading higher education sector can help make more good school places available.