of course i am very much in favour of backing teachers publicly - at least in front of children. the behaviour towards this woman is disgusting.
the request is at first glance polite - reasonable is another thing entirely. she is passive aggressively imposing her will and personal beliefs. its an incredibly frustrating and underhand tactic. and it takes people in, as amply demonstrated here.
Passive aggressively! That's an oxymoron that Spike Milligan would have been proud of! As for her will and personal beliefs, are you challenge generally accepted medical theory that, not only is smoking bad for the smoker but that it also harms those that 'passively' smoke. There are plenty of doctors that smoke but I've not heard of one that doesn't accept that smoking is harmful.