An even less elevated motive is cited by people who only visit top schools - namely the fear that these children may soon be in a position to sack them. And lowest of all is the advertising man who says he visits six schools a year to pick up the latest vibe on how to sell rubbish to the rising generation.
Anyway, for whatever reason - duty, vanity, curiosity or self-interest - we agree to go in. If the school is of a nervous disposition, we are put through the glacially slow process of getting a Criminal Records Bureau disclosure, which makes it seem all the more portentous.
For what you have to know, teachers, is that we are terrified. Petrified. You are used to classrooms, and that row of openly judgemental little faces scanning you from head to foot, waiting for you to show weakness - and, in the case of the older girls, mercilessly pricing your outfit.
But we aren't used to this. We know the ways of adults, with their highly developed techniques for disguising their contempt and boredom in our company. The naked honesty of children unnerves us.
Primary schools are easier because you are not quite so tempted to swear. (Look, teachers, you would not believe how frightened we visitors get at the possibility that we might accidentally use a bad word in a classroom and get drummed out in disgrace by the head. Oh, and we're scared of headteachers too.)
But secondary school talks are truly terrifying. You falter and tremble as you begin explaining what it is like to be a radio presenter, journalist, engineer, explorer or whatever. I suspect that the engineers and explorers have it easier than media types because the questions they are asked are more often factual, though this isn't always a bonus - a female Indian explorer at a school in Lincolnshire was asked: "Have you ever put your head in an elephant's mouth?" By great good fortune, it happened that she had.
But, as a journalist, when I have finished droning on about a free press or BBC impartiality, what usually happens is a dead silence, and then a hand goes up and a voice says: "Have you met any really, really famous people?" So you confidently list the politicians and authors until the stony stares alert you to the fact that they mean an Arctic Monkey or a Beckham.
For some years I managed to impress them with the fact that Damon Albarn of Blur met a girlfriend on Radio 4's Midweek, but I fear his lustre has faded. I did once, with a particularly insistent questioner, cite the Duke of Edinburgh, but only one of the GCSE group knew who he was - and she asked: "Was he, like, really, really old and wrinkled?" Luckily, the teacher intervened.
Despite all this, usually it goes better than you think it will. Often this is due to the skill of the teacher, who unobtrusively chucks in supplementary questions. Sometimes (lately, in fact, in another Lincolnshire school) it is a blast, and the children are so full of fizz that you leave walking on air, and spend a short, mad period resolved to retrain as a teacher. Other times, you are just glad it's over.
But it's a great lesson in knowing your place. I asked my daughter - the most recently educated of my family - what pupils think of these sessions. She looked at me as if I was mad. "It doesn't matter who it is," she said, "if it just breaks up the routine."
Libby Purves, Author and presenter of The Learning Curve on BBC Radio 4.