Les Ebdon said that the government's decision to publish information about what pupils do after leaving school risks "undue pressure" being put on students to study unsuitable courses.
Instead of simply focusing on getting more pupils into top universities including Oxford and Cambridge, schools should consider what is best for pupils, including vocational courses and apprenticeships, Professor Ebdon told TES.
His comments follow repeated criticism from Michael Gove, the education secretary, that too few pupils from poor backgrounds win places at elite universities, particularly Oxbridge. The Department for Education published the "destination data" of pupils for the first time this year to highlight which schools are successful in sending their pupils to such institutions.
Mr Gove has praised the success of state schools such as Mossbourne Community Academy in London that send large numbers of pupils to Oxbridge. He has said that there is a danger of other schools accepting that children are going to do badly, making them "the victim of the bigotry of low expectations".
But Professor Ebdon, whose took charge at Offa in September, said it was important for schools to be judged on whether they were encouraging students to take "the most appropriate route to realise their full potential". He expressed dismay that society "really undervalues apprenticeships" and engineering-related courses.
"One of our problems is there's such a dreadful snobbery about whether people go to university or which university they go to," he said. "I would hate to see that work through into undue pressure on schools."
Professor Ebdon said that students should be "choosing the subjects in which they excel and enjoy" rather than feeling pressured by their school, the state of the economy or their parents' ambitions.
He said he had been struck by how parental pressure influences black and minority ethnic students to apply for medicine and law courses when attempting to win places at Oxford and Cambridge, despite those courses being some of the most over-subscribed.
"This is one of the reasons that some groups are underrepresented at some universities," he said.
"We should be treating people as individuals. This perceived feeling in our society that to be a doctor or lawyer is a high-status profession that black people aspire to for their children... there's nothing wrong with it, but the most important thing is that students should be encouraged to fulfil their full potential in whatever subject that is," he added.
The appointment of the former vice-chancellor of the University of Bedfordshire to Offa was steeped in controversy, with a number of Tory MPs opposing the move.
Before his appointment, Professor Ebdon criticised the government's higher education policies and threatened to use the "nuclear option" of financial penalties against universities that fail to widen their intake.
The 250 leading independent schools, which dominate successful applications to elite universities, have criticised some institutions for using "contextual data" and making lower offers to students from low-performing schools, a policy that Professor Ebdon supports.
But he told TES that private schools have "nothing to be particularly fearful about" and said if their students attained good grades, they would get in.
"Universities can now let in as many students as they want with two As and a B, so hopefully that particular argument, which always was rather spurious, will be defused," he said.
He added that encouraging universities to look at the school backgrounds of applicants had "levelled the playing field" to an extent. "It's terribly important that we don't ignore the potential for excellence for pupils who may have had disadvantage in their school," he said.