Because it's a nationalistic thing to insist that all languages spell your country's name in the script and spelling of the source language. It's a stupid move by the Erdogan government to get people to stop thinking about türkiye birds when they think of the Turkey country. Other countries get by just fine.
Germany, Alemania, Deutschland.
Mexico, Messico, Méjico.
Japan, Nippon, 日本.
China, Zhōngguó, 中国.
Every country gets by getting called different things in different languages. But Turkey insisting on the spelling just because they don't want to be associated to türkiye birds, where the birds are literally named after the country, is a silly move designed to stir nationalistic pride for their near totalitarian government.
One funny thing is that in Portuguese the word for turkey (the bird) is Perú… also the same word as the South American country. Turkey is Turquia though…
I'm from a language where you'll never get it right, and most people are pragmatic and don't care about names being the way our mothers do. That's a very Western thing.
Forcing us to try to teach you our language, or half-way butcherings, are considered obnoxious. Go with the English pronunciation. Do anything half-reasonable-sounding, and it's okay too. Don't visibly struggle each time you try to say my name.
For my name specifically, there's also an uncanny valley phenomenon. My name pronounced obviously wrong by an American doesn't raise flags. Americans mispronouncing my native name sounds horribly wrong.
Not a Turk here, but I'm guessing it is equivalent to using latinx or Latin@. It is a signal that you are from a bubble that is out of touch with your intended audience. Most Latin people don't use these terms and don't particularly care for them, so it signals that you are more aligned with a third-party then with Latin people.
What? If you would try to say my country's name in my native language instead of the English version when speaking English I would think you were a nutcase.
Similarly my given name has an English pronunciation that I prefer people use when speaking English. Someone trying to pronounce it natively without being native would feel extremely awkward and not respectful at all.
I find that impossible to achieve and believe others do. I have no expectation people getting my name right because, apart from other reasons, it contains sounds that do not exist in many standard languages. It would literally require training one to be able to produce new sounds, and that is just not practical at all, not to mention outright impossible for many to do accurately. I guess it is good to try to pronounce things good enough, but "correctly" I doubt.