Parents, governors and teachers often hate Greek and Latin, says a new document from the Qualifications and Curriculum Authority.
But schools must not succumb to prejudice and "throw away 2,000 years of history".
Writing in Classics in the Curriculum, university lecturer Dr Peter Jones says that ignorance and personal bias are partly to blame for the beleaguered state of these erstwhile pillars of learning. Only 12,000 students a year take GCSE Latin.
Many adults, he believes, are put off by their own grim experience of Latin verbs and baffling translations.
"It was indeed hard to see what was to be gained from grappling with sentences about queens attacking roses with ditches and arrows while slaves loved the clear voices of the girls," Dr Jones writes.
But, he argues, the subjects have changed. Latin and Greek should be seen as opening pupils' eyes to the existence of radically alternative languages and worlds.
Classics in the Curriculum, which was due to be released this week, was jointly published with the Joint Association of Classical Teachers.
It springs in part from the personal interest of Dr Nicholas Tate, QCA chief executive, who is keen to support the traditional humanities. But it is also an indication of the authority's overall determination to promote curriculum breadth.
The document argues, too, that Latin and Greek have a part to play in the current campaign to improve children's English.
Dr Jones, one of nine contributing authors, writes that languages with a very different structure like Latin can help grammatical understanding:
"This is ... an important spin-off at all social levels, as American research has shown. By mastering a vocabulary with a powerful influence on English, pupils' chances of success in all subjects in school are increased."
Moreover, he says, classical literature is worth reading in its own right, from Homer through to the satirists Juvenal and Lucian.
"Its literary quality and agenda setting coverage of a huge range of still important issues have recommended it for more than 2,000 years."