As far as I can tell, the main driver of family expenses in mortgage/rent and keeping up with the Jones' (but I don't know if the last is a uniquely Bay Area problem). Unfortunately, many families reach for the max mortgage someone will lend them, which keeps expenses and housing prices going up. If you pay $50k/year ($4k/month) on a $850k mortgage and $30k/year in taxes, it's easy to see how $120k/year is low-income. The remaining $40k divided by 4 people = $833/month per person for food, clothes, transportation, insurance, etc. Not poverty, but not high living either.
I know many families in the area that complain about the high cost of living yet frequently carry debt for that new car, or a credit card balance they can't afford. It's a self-generated problem that keeps going.