Reality,
I never saw this post -- have no clue when you posted it but I wasn't "ignoring it."
I had never heard of Avril Lavigne until reading your post -- you need to remember that I teach voice and correct singing and pop don't usually go well together. There are only a few singers out there who sing properly -- some do some things better than others but most do almost everything wrong.
Avril, from the little I listened to, does some things right (frontal placement rather than singing in the back of her throat) but it's pretty obvious she doesn't have great diaphragmatic support and there's a lot of tension (for several reasons) in her voice. Of course, people who want to make it in the music industry today don't sing correctly -- most people don't want to listen to people singing correctly. You CAN sing correctly and sing a lot of different styles but usually it sets you apart and it isn't what most people enjoy. For instance, Whitney Houston is one of the better singers when it comes to singing correctly (she's close) but most don't want to listen to her either. Today's popular singers seem to be more 'breathy' than not and you won't find vocal teachers teaching that.
As for a vocal teacher -- honestly, I forgot exactly what I posted before but most vocal teachers (who are properly trained -- there are a TON of vocal teachers out there who are teaching simply because they have been singing all their lives -- that's like hiring a mechanic to overhaul your engine simply because he has worked on his own car in his garage) teach correctly -- but there are two schools of thought in vocal teaching -- frontal placement and back placement. Personally, my definition of singing is "sustained speech" and that means your placement when you sing is the same as when you speak -- simply sustained via the diaphragm. For instance, take the three tenors -- Pavarotti, Domingo and Carreras -- here are three widely successful opera singers with three totally different placements -- Pavarotti is a frontal placement singer (i.e. IMO, has great expression, greater understanding of words and greater control of volume), Carreras is the complete opposite (rear [back of the mouth] placement which results in a "covered" sound that lacks expression, is more difficult to understand words and doesn't allow as much volume control, Domingo is a hybrid -- he is between the two in placement). A lot of this goes to placement and where you teach (or are taught) -- different schools have different schools of thought. Thankfully, most are teaching frontal placement today.
If you really are looking for a vocal teacher to teach you properly, go in and ask them about placement and the mechanics of singing correctly. Ask them to model the difference between frontal and rear "placement" of the voice -- then judge for yourself. IMO, frontal placement allows for individualism (actually sounds more like the person) but there are schools who want everyone to try and make the same sound rather than having to blend voices -- I'm not a proponent of that thought.
Hope that helps.