I grew up in a family of Eastern Europeans, who all seem to have a fondness for cooking everything to death and then some. My mother is the worst culprit of this bunch. (God bless her, she actually is a very good cook, but I don't trust her on roast or grilled meats.) She was convinced that, no matter what, pork tenderloin will always be dry and always requires a lot of sauce to cover this defect up. I was absolutely astonished when, while learning to cook myself, I discovered this was indeed not the case if you knew how to prepare it: enough so its cooked through but with a tinge of pink inside. One of my favorite dishes now is a simple pork tenderloin encrusted in crushed fennel, black pepper, and salt. A little gravy on the side, perhaps, but not necessary. Both juicy and tasty.
As for convincing people, I think people like my mother are beyond change. My brother prepares the steak for her, since he is the king of marinades, and I find them pretty much essential for making well-done steak edible. Myself, I'm a sprinkle of salt-and-pepper kind of guy, for the most part.
However, I did manage to lure a girlfriend of mine away from the Dark Side. We were having a cook out on the banks of the Danube (she's Hungarian) with a couple of folks, and she insisted on having well done steaks (as is usually the case out in Hungary). Somehow, we ended up with all the steaks no done more than medium rare. Not wanting to waste a steak we paid good money for, she bit into it. Her hesitant look of disgust turned to pure delight: "Wow! How did you make this steak so tender!? It's wonderful!" "That's what happens when you buy good meat and don't cook the life out of it." Since then, she has always been a medium-rare girl. I'm proud.
My brother and cousin, too, are beginning to come over to the Medium Rare Side. I've got my cousin as far as medium (he's a lover of sushi/sashimi, so I'm surprised he doesn't like his meat rare), and my brother actually does enjoy good cuts of beef medium rare, from time to time.
My problem with well-done steaks are they just don't taste like MEAT. The red juices just have this overwhelmingly beefy flavor that's fantastic. I don't understand why people want to cook this flavor out. Also, the texture of medium-rare meat is much more satisfying than the grainy chewiness of well-done. It's not that all well-done steaks are tough--many can be prepared to a decent tenderness. It's just that they're grainy.
Another problem is the quality of beef. If you've ever had a mediocre cut of medium-rare steak, I wouldn't be surprised that you cook the living daylights out of it. That was one problem in Hungary--it was difficult to find a good grilling cut. You had to tenderize every cut of steak except filet. In this sort of environment, it's no wonder people were taught to eat beef fully cooked. It was next to impossible to eat rare steak--it just didn't break down from all the chewing.
Imagine trying to eat sushi, if all you know of fish is those crappy little filets you get in Dominicks.