Despite the fact that well-done steak is tough, dry and flavorless, there will always be people who insist on having their steaks cooked that way. You can reason with them all you want, but it's not going to change their minds.
You could take your beautiful strip loin or porterhouse steak and cook it well-done for them. But this is a crime against meat. Don't ruin your expensive steak this way. After you've gone to the trouble of selecting the best meat, seasoning it properly and prepping it for the grill, the last thing you should want to do is destroy it by cooking it well-done.
What's so bad about cooking a steak well done? It all comes down to temperature. The longer you cook a steak, the hotter it gets, and as it heats up, the muscle fibers get firm and all the juices cook out.
The result is that the interior of a well-done steak is a uniform gray color, and the steak itself is tough, chewy, flavorless, and dry. This isn't cooking; it's arson.
Why Not Well-Done?
A well-done steak is defined as a steak that's been cooked to an interior temperature of 160 F or higher.
What happens when a steak—any steak—is incinerated to that extent is that it becomes tough and chewy and devoid of any juiciness whatsoever. It could be the finest, dry-aged, lusciously marbled USDA Prime beef. But if you cook it to 160 F, it's compost.
What about food safety? Isn't that a good reason to cook steaks all the way through? Actually, dangerous bacteria like E. coli don't live on the inside of a steak. They might live on the surface of a steak, but cooking the outside of the steak will kill them. Burgers are another story. To be safe, ground meats should be cooked well-done. But medium-rare or even rare steaks don't present any particular food safety hazard.
Having said that, you're not going to win an argument with someone who, for whatever reason, wants their steak cooked well-done. Plus, it's bad form to argue with your guests, right?
Your Guest's Absurd Request
If your guest insists on a well-done steak, there are a couple of tactics you could employ to deal with this difficult situation. You could try to cook the steak medium-well, which is one notch less done than well-done, and hope they can't tell the difference.
A medium-well steak is cooked to an interior temperature of around 150 F to 155 F. The interior will be mostly gray but with just a faint streak of pink at the very center. If you dim the lights when you serve it, they might not notice.
Even if you could get away with it, though, this is still a waste of a good steak.
Your best bet is to buy an inexpensive steak, something tough and lean like a sirloin steak, round steak, or rump steak. Cook it over medium heat for about 12 minutes on each side, and serve that to your guests. It's going to taste like a cinderblock anyway, so why throw away good steak (and good money) on someone who'll never taste the difference?
This isn't snobbery, it's economics. There's really no excuse for cooking a good piece of meat past 145 F.