There is definitely a large number of folks for whom that is true. Reasons I’ve personally been given:
- who knows what quality this restaurant beef is?
- They don’t want to see “blood” in their food
- They’re afraid of “pink” meat
#1 might be an issue if the place is sketchy I guess, but mostly not an issue. 2/3 are psychological so you’re not likely to change minds.
My reasoning is pretty hilarious: as a kid, no one told me what the different doneness names meant, so I used to order “medium well” because I thought it sounded the coolest (this lead to me not really liking steak or roasts unless they were drowned in sauce, until my adult years when I finally had proper medium rare steak).