Airbags are not designed to deploy in every collision or car accident. This is contrary to what I thought and had heard when I was younger. I believed that in every significant car crash with an impact that the airbags would deploy, saving me from getting jerked around in the car or hitting the steering column. This is not actually the case.
The designers of airbags have designed them in such a way that they only deploy in a specific set of circumstances and under certain speeds. Normally this is a direct front end collision for front airbags. They normally are not supposed to deploy from a glancing impact. This is an area of the law though, where each case is very specific. If you need advice about this, you need to speak to an attorney who is very knowledgeable in this area.