When are you no longer a beginner?

When Fred Beckey invites you to go climbing.

I'd say it has nothing to do with what rating you climb. 

When you can confidently lead an excursion and take care of everything yourself is when I'd say you're no longer a beginner. So you could be a 5.13 sport climber and have led hundreds of sport climbs. But if you've only followed trad climbs and couldn't lead them, you're still a beginner trad climber.