First of all, just because you get selected to go to TOPGUN doesn't necessarily mean you are the "best of the best". I may get eviscerated saying this, but I've known a lot of great sticks that never went to NFWS that were far better pilots and officers than their counterparts that got selected to attend. Their timing just wasn't great. As far as VFC-12 or VFC-13 were concerned, we tried to send as many of our pilots to the adversary course as we could because it helped our credibility. When I was there, we were fighting many regular Navy types who considered us nothing more than a flying club, i.e. just a bunch of reservists who only flew on weekends for fun. Having that adversary patch on your sleeve gave you a little more respect/status in the debrief. I mentioned earlier we had about 90% of our SELRES who attended the adversary course. Let me modify that to having attended either the adversary course or the regular course when they were in their fleet squadron. Some even did both.
How did VFC-12 get that name/designation? They were originally VC-12 and performed the normal VC type mission - towing banners, providing AIC support, etc. They gradually became more involved in the adversary side of things and somewhere around '87-'88, the push was on to get them re-designated as a full-fledged fighter squadron. At that time, VF-43 was a regular Navy adversary squadron at Oceana, and VF-45 was doing the same thing in Key West. Someone made the proposal to change the name to reflect the increase in the mission as an adversary squadron and with the help of a few regular Navy supporters, low and behold they became VFC-12, Fighter Squadron Composite TWELVE. Why it wasn't Fighter Composite Squadron, I don't know. The same thing happened with VC-13 becoming VFC-13. I was the A-4 NATOPS Evaluator for COMNAVAIRESFOR at the time, attached to COMFLELOGSUPPWING at NAS Dallas, who, at that time, had operational control over 12 and 13 because they were considered reserve support squadrons. And now you know the rest of the story.