The guy with bigger arms always wins the Arm Wrestling Contest - NOT. If size equaled strength, this would always be the case but it's not and it doesn't.
As some have mentioned in previous posts, the Muscle Builder's main goal in the gym is to breakdown the muscle(s). This may be accomplished with heavy weight but is not necessary. It is IMO necessary to keep the muscle(s) confused. When your muscles aren't confused, they adapt and get stronger. The body naturally tries to prevent the muscle from being broken down.
Back in High School I saw a video (not PI) of Lou grunting and straining over a seemingly light weight alternate dumbbell curl session. I don't remember the exact weight of the dumbbells, but I was shocked because I could do sets with the same dumbbells. A friend (Football Player turned Trainer turned Bodybuilder) then explained to me that training for size is not the same as strength training.
After that I changed the focus of my routines (which are actually anti-routine) to promote muscle fatigue/breakdown. And of course anti-routine could also include heavy lifting, BFT, etc. but only for the sake of changing the routine for confusion.
At this time (18 yrs ago) I worked out with 3 friends that I grew up with. We were all at or around 5' 10", 165 lbs. We were all thin, hard gainers with fast metabolisms. Our diet and training up until this point were nearly identical. At this point I changed directions.
After that, my friends consistently increased their strength (one rep max, etc) at a faster pace than myself, while I consistently gained more weight, size and development than the group. I reached 200 lbs when they were approaching 185. A couple years later I reached 220 as they ranged from 190-200. My friends ate just as good (6 meals, 1+ lbs P, etc) and trained just as hard, some would say harder. And they gained some serious strength over the years. At 185lbs they were all benching at least 320lbs.
My goal in the gym was simple: I wanted to feel sore everyday, just like when you return to the gym from a long absence.
The problem with training for size is that you may see a drop in strength and that idea doesn't sit well with a lot of Lifters. Just the idea alone would drive some crazy. I think a lot of guys argue that lifting heavy is the way to go because they wouldn't even consider another option or method.
Strength does not equal size. However, a Lifter who has trained for size can change their routine and quickly gain and develop strength. After all, he has bigger muscles.