Sure, or elf-like people of one kind or another, or a culture that is tuned toward what the player wants out of playing an elf. No way to know without having the conversation.
The player insisted they be able to play an elf. They refused a human with elf-like tendencies. The setting was humans only so no other elf-like people were available, just humans. They insisted they be allowed to play an elf because the core rules of the system we were tentatively supposed to use has elf as a playable race. The player completely refused to play a human, they would only play an elf.
What compromise could there be?
Don't worry I'm happy with the outcome as the player displayed several personality traits that lead me to believe they would be a "problem player" in the future. The other players confirmed my suspicions in later conversations after the player stormed off.
Bonus for me as I easily convinced the group to abandon D&D and use a different system more suited to running a GoT pastiche. The only hangup is that I now have a group that is unfamiliar with the system I will be using. Bonus though, as I find those new to a system can often be convinced to just ignore it and focus on describing what their character is doing. We will see I guess, two of the players have some familiarity with non-D&D games, so at least the whole group won't be stuck in a D&D only mindset.
Another bonus is that the ousted player already found a spot in a different game and, I was told, really is going to play a Teenage Mutant Ninja Turtle! Honestly I don't think I could run a D&D game with a Turtle Person in it and not constantly be laughing and making TMNT jokes.
So good for the ousted player, they will be far happier in their new group! Good for me cause I avoided having to use D&D, a system I really do not like! Good for my group as we can now play the campaign we all wanted to! Good for everyone!
See, sometimes not compromising and giving a player the boot works out for the best! Yay!
Also, I did compromise on my "no magic users" policy. I didn't want to have the PCs using magic right away. However one of the new players really likes mages, so we compromised. He agreed to only have subtle magical abilities that could not be used in a combat situation, so I allowed him to play a magic user. Bonus Fact, the magic user in my group is also the second best swordsman, second only to one of the Knights, but ahead of the other Knight and all the Nobles! Yay! Not using D&D opens up a whole world of character possibilities that absolutely can't happen in a D&D game. Yay! Diversity!