It was an organized club my high school. Some of the hottest girls in my class were members and "helping out" with their new baby calf was a perfect excuse to stop by and say hi.
Don’t know how long ago that was but FAA during my time in high school (early 1950’s) was classroom study with maybe a couple of field trips thrown in. We lived in a rural area in upstate NY and all the boys from the farms were in the FAA. What you’re describing would fit more 4H than FAA...Girls did not enroll for FAA class..I think probably because all the guys there were our friends and not of any interest other than that. These were the guys who drove to school in family pick ups.
Maybe there are other “farm” girls here also. I found it interesting after graduation that all the “town” girls married farm boys and all the “farm” girls married “non farm” guys and met partners in college or the working world.
IMO the “clubs” listed in the original post were extracurricular - not on school time - gun club etc.
Looking back 70 years, perhaps “club” would fit as the yearbooks always had group pictures of the FAA class as well as band and glee club etc. Interesting.