Meaning of "I've been doing this long enough to drink"

This law varies by country, but in the US you gain the right to buy alcohol at age 21.

The idiom comes from that law. If you've been doing something long enough (in this case 21 years) you earn some extra rights. A newbie to a field might not be cut the same slack as the old hands are. You don't earn the right to criticize something your first day on the job, but when you've been in the field for a long time you earn that right.

To me, that comes across more as "I've been doing this long enough to turn to the drink". That is to say that the repetitive nature has driven a person to alcoholism, though said in jest. I don't know how much of a British thing that is though - joking about depression and alcholism.