It seems that for some people, if you don't like your steak rare, you are also not a big fan of steak. I can understand the desire for fully cooked meat, but I also wonder if that also prevents you from having it at its best. They say that if you don't like seafood, you just haven't had good seafood. Perhaps that applies to steak too.
When I order meat at a restaurant and they ask how I want it cooked, I'll either say "as rare as is safe" or "however the chef recommends". I won't shy away from eating raw meat. I love sushi, and on the rare occasion that I get top quality beef, I'll eat that raw too.