Yes, there are "no drop" rides and then there are "well, we don't drop people who are a *little* out of shape," or "we don't drop people in April and May, when we're out of shape," or "we don't drop people their first time out, but then they're supposed to get in shape..." And these are usually nice folks who are well-intentioned, too. I can sorta tell by their gear and the look in their eyes
And then, of course, there's the "posted" average speed issue - good riders always underestimate (and besides, "average speed" of say 14 means you have to spend a fair amount of time going 16 or 17) that and the distance.
Couple of choices: Keep showing up to those "no drop" rides and ask if somebody is willing to actually not drop you; generally somebody else will show up on some week or another, and then you can ride together and feel a little less dropped; there's often a "critical mass" thing where if one or two people hang in there, then a core group forms and soon there are 8 of you and so 3 or 4 will be on any given ride and people don't feel as discouraged.
Of course, then what happens is, since you're riding that much more often, you get stronger without realizing it and drop the next newbie who shows up becaues "hey, I'm not in shape, I wasn't going that fast!" ... except you were ... so don't forget where ya came from ! Be willing to sacrifice your good strong ride every once in a while to saunter along with people who are still working hard to go at that pace. (If you're *really* good at it, you set it up so somebody's riding behind them at least part of the time.) Or take a beater bike that *is* that hard to get rolling (or if the newbie has fat tires or something else that slows 'em down, trade bikes for a while!) I've found that there are more people willing to take their turn bringing up the rear when there are a couple of people setting an example who they know could go faster if they chose.
Another choice is to figure out how fast you have to get and train for it. When I wanted to 'graduate' to our "Level 2" ride (which advertised as 14 but was often 16-18) I picked a loop and timed myself and when I could do 12 miles at 15 mph I figured I was ready.
And thirdly you can join the club and lead a "no drop" ride. I started mine when we were bemoaning that there was only one "level 1" ride, with the promise that I couldn't do much else, but I could promise to "show up and ride slowly." Sometimes now we've got more folks out there than the fast group