I agree that, "No, thanks," is all that is needed. For those who knew me as a drinker:
"It just wasn't helping me in any way in my life."
"I feel so much better without it."
"I've outgrown my partying days."
"I've decided to focus on my health and fitness," (of course, then there's health and fitness to focus on...)
"I'm taking a break from it to see how I like a completely alcohol-free life." You could use that for the next 40 years
- "Oh, yeah, I'm still taking a break."
"I don't like how I feel when I drink," or, "I don't like the day-after feeling."
I don't talk to people about the "why." They are free to think what they like. I give them whatever suitable answer comes to mind at the moment, but I don't use the word alcoholic anywhere except here.