What is the deal with swearing, and around children?

I witnessed a very ordinary public scene in Chicago a few months ago: I was sitting on the El train, when a street person began soliciting clothing to the train's riders. Someone spoke up, commenting, "You know, you can get in trouble for that." To which the street person responded, "Fuck trouble, I am trouble." An older woman then added, "Please watch your mouth, there are children here."

I had always assumed that it was impolite or inappropriate to swear in public, especially around children, but that scene led me to consider the reasons for my assumption and the nature of the social rule. And so my theorizing began. Perhaps parents would like their children to grow purely/innocently. Until they're older at least, and know right from wrong, good from bad language, etc. Such a classic and uselessly unrealistic ideal. Swearing is common enough that most children in the U.S. will witness plenty of it randomly throughout their daily lives. For parents that wish to raise their children "properly" (not really sure what that might mean), I would think that the best course of action would be teaching the children the meaning and uses of swear words, and to let their own experiences further support (or contradict) the transferred opinion.

I think that it's generally better to know and understand, rather to not know. Even for, especially for, the subjects that people may consider impure or unpopular.