Your parents have no more right to "quiz" you than any other people.
If you say "No thanks" and your parents push it, keep saying that. If they get pushy, a simple, "Why does it bother you?" seems to work. Then they have to actually look at themselves and why it bothers them. I think a lot of times, people think you are judging them. (So?) There are lots of other things to say, too, like, "I don't like what it does to me." "I'm just giving myself a break" etc...
But this thing about your family being drinkers, that's them. You are a separate person. My family drank. For 18 years of my sobriety I went to family gatherings and no one held me down and forced it down my throat. They did continue to ask me, every time, if I wanted one.