same thing happened to me once. Well minus teaching the noobs because I don't owe them anything. I did something so simple, this a no brainer....

1. Loosen the set screw....
2. acquire black drywall screw and cordless drill (on the LOW setting). Drywall screw is small and thin enough, with sharp enough threads, that it shouldn't cause the plastic to expand too much.
3. Screw into the remaining piece of fin, only need to get a couple of threads into it
4. Using any sort of pliers, grab that thing and start pulling directly out of the hole. Don't wiggle side to side because you can crush the white stuff that holds the fin plug in place (F*cking nightmare to replace that...)
5. Install new fin
6. tighten set screw...