Better the devil you know
An even lesser 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.
For whatever reason, we agree. If the school is of a nervous disposition, we are put through the glacially slow process of getting a criminal records 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 judgmental 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. (Teachers, you would not believe how frightened visitors get at the possibility that we might accidentally use a bad word and get drummed out in disgrace by the head. Oh, and we're scared of headteachers too.)
But secondary school talks are 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 their questions 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 fortune, she had.
But, as a journalist, when I have finished droning on about a free press or BBC impartiality, what usually happens is silence. Then a hand goes up and a voice says: "Have you met any really famous people?" So you list the politicians and authors until the stony stares alert you to the fact that they mean an Arctic Monkey or a Beckham.
I did, with a particularly insistent questioner, cite the Duke of Edinburgh, but only one of the group knew who he was - and she asked: "Was he, like, really really, old and wrinkled?" Luckily, the teacher intervened.
Despite this, it goes better than you think it will, often due to the skill of the teacher, who unobtrusively chucks in supplementary questions. Sometimes (lately, in fact) 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 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 is an author and presenter of The Learning Curve on BBC Radio 4.