Read Maty Ezraty's response:
What a brave question!
This is a painful and important lesson to learn: Never teach what you do not know.
Admittedly, this advice poses a dilemma, because we need to evolve and be willing to grow. But it's not a good idea to teach new techniques or change your teachings immediately after taking a workshop. You have to practice new information long enough to truly digest it and "own" it for yourself before introducing it to your students. It is very easy to misunderstand new teachings, or to be misinformed.
Having said that, you now have a responsibility to your students, and it is clear that you are genuinely concerned for them. Truth, or satya, is one of our yoga vitamins, essential for good practice and teaching. We all make mistakes, and if you can admit that, your students will value your courage and honesty.
You can correct your situation by simply teaching the backbends differently from now on, or you could come right out and say that you are taking a different approach based on your practice. You do not need to feel bad or apologize. Simply state that you are taking a new approach and move on!
I doubt your students will leave you; more likely, they will respect you. Either way, it is not important. Do the right thing. Speak the truth and let the rest fall into place!
Maty Ezraty has been teaching and practicing yoga since 1985, and she founded the Yoga Works schools in Santa Monica, California. Since the sale of the school in 2003, she has lived in Hawaii with her husband, Chuck Miller. Both senior Ashtanga teachers, they lead workshops, teacher trainings, and retreats worldwide. For more information, visit http://www.chuckandmaty.com.