It's because they know even one casual drink can lead them down the same path they were on previously, so it's a reminder to themselves and others. It might also be something of an absolutionary statement, where they feel guilt for their past "sin" of drinking and feel the need to label themselves à la The Scarlet Letter to atone for their sin and obtain absolution.
Maybe it is sometimes part of a person's identity. But people who have quit using tobacco or other drugs are typically called "ex-smokers" or "former users/addicts", respectively. (Even though "smoker" is still a somewhat "cool" identity in popular culture, with many movie villains - and some heroes - still smoking.)
Without trying to make it sound judgemental I know literal dozens of people who stopped smoking and it hardly comes up in conversation anymore - I think I have like 2 friends left who smoke, out of... more than 50%? And several of them smoked for 10 years or more.
Maybe it's because most people don't just randomly are offered cigarettes or because it went from a "50% of the population" to "10% of the population in this age group".
I'm not saying that sober alcoholics are making a big deal out of it, it just feels different - maybe because it is seen as a lot more problematic than being a smoker? Or harder to quit. Or because it's rarer.
Good point - cigarettes are increasingly harder to find, and are banned in many places (restaurants) where alcohol is readily available, and associated with sociability. There even seem to be more marijuana shops vs. tobacco shops (or liquor stores for that matter) in some places, and the former are advertised while tobacco advertising is banned. On the other hand, while smoking may be in decline, I still see (and smell) vaping everywhere.
