A while ago Nathen wrote a blog post about how his dentists' instructions for optimal tooth brushing has changed over the years.
As someone who has taught tooth brushing both as a parent and in the preschool classroom, I can sympathize.
There are actually several different "schools" of tooth brushing technique. You can read about some. They have names like the Bass Method, Stillman Method, and Chartes Method.
Why don't dentists agree which is best? No one follows them rigorously enough for an experimental study.
It was tried once. Dentists were the subjects.
The only meaningful conclusion was that even dentists do not use any method properly and faithfully.