How did this myth begin? The Tooth Fairy is often associated with Santa Clause, but is presumably a more recent bit of folklore. Was the Tooth Fairy an American invention, or a hold-out from European legends?
There are two excellent articles dealing with the tooth fairy in Peter Narvaez, ed. The Good People: New Fairylore Essays (1991). Tad Tuleja "The Tooth Fairy: Perspectives on Money and Magic" and Rosemary Wells, "The Making of an Icon: The Tooth Fairy in North American Folklore and Popular Culture." I recommend them.
Tuleja rightly points out that origins are unclear. But the author suggests that the widespread European "tooth mouse" is a good candidate for the source (while referring as well to Italian and French candidates and/or influences). The tradition was to offer milk teeth to various animals, but especially the mouse because the animal's perceived strong teeth, there being the hope that this strength could be transferred, magically, to the child whose new, permanent teeth were about to emerge. Taleja maintains that a fairy with a variety of names (but not with the word "tooth" being presence), occurred in the 1920s and 1930s in America. The true "tooth fairy" did not emerge until after WWII, apparently appearing for the first time in indexes in 1949 in an article in Callier's magazine. Taleja credits the emergence of the tradition to post war affluence, "The Cult of the Child," and media encouragement.
This is outside my research area, so I can't evaluate the argument more than to say that it is well presented and makes sense. I hope this helps.
Not discouraging more contributions, but you can get started with the responses on this previous thread: