I've found it's far more difficult to explain my reason for abstinence to family members. There are two reasons for this. One, the majority of my family members are heavy drinkers and/or alcoholics. Two, my family members always denied my drinking problem, including their own.
When I told my mother I couldn't control my drinking, she said, "You're completely in control of you drinking. Just learn to drink moderately. You don't have a drinking problem." However, I have tried moderation numerous times and failed within a matter of days. When I told her this, she claimed I wasn't trying hard enough.
My friends seem to understand my reason for abstinence far better than my family members. It helps that my friends rarely drink (most drink 0-2 alcoholic beverages a week).
To be honest, the best thing to do is be selfish and ignore your parents. It sounds rude on the surface, but maintaining sobriety is a miraculous achievement. Think of it this way: you'll be alive longer to spend time with them.