once again needing to remind some people that mispronouncing foreign words isn't just about not knowing how to say it; if your language doesn't have that sound, in many cases you can't hear it properly. You won't be able to hear yourself say it wrong because you probably can't distinguish between the sounds a native speaker can. It will sound right to you and you will be wrong.
Most languages use relatively similar sound inventories overall, but make distinctions others don't. And the way the our language centers work is they group these sounds together, allowing us to recognize that things within a given range constitute a recognizable phoneme. If your languages groups together sounds another language makes a distinction between, your brain cannot tell.
So everyone on those posts congratulating themselves for looking up pronunciation and saying "It's Not That Hard?" Surprise, you might have still got it wrong and can't even tell. You can look up the IPA chart and still flub it completely because what sounds right to your brain and what a native speaker will understand are totally different things!
"I might have butchered that, please let me know" is sometimes an excuse for lack of research, but it is, unfortunately, also a much more accurate self-assessment than confidently fucking it up after mouthing along to a wav file a few times.
This is one of the reasons that, historically, many people would take on or be granted new names if they stayed any length of time in another culture; it's very common for the names from one language to simply not map to the sounds of another!

(I first need to say that it is folly to overexamine a slogan, and the slogan as it stands is never intended to be examined; it is a tool for provocation and a rally to do better, and can never be “incorrect.” I am not criticising the intention of the slogan.)
When Black Americans have addressed the genuinely shameful failures of white Americans to pronounce Black names, it is, firstly, absolutely necessary. This has been done in the past with the slogan, “white people can pronounce Tchaikovsky and Schwarzenegger.”
This is intended to highlight the entirely correct point that white Americans have made more efforts to address names that are considered “foreign” and “difficult” but are associated with “white” cultures, than to address Black names. The slogan is provocative, useful, and highlights the hypocrisy of white Americans. It is a challenge to do better. Because Americans often perceive z’s and v’s to be “foreign” and “difficult” it is an especially pointed dig.
However. Let us briefly lump together Americans, all English-speaking Americans of various backgrounds dialects, into one American lump and stand back.
Respectfully: you HAVE to be American to believe that Americans have learned to pronounce “Tchaikovsky” and “Schwarzenegger” correctly.
Although Americans firmly and confidently believe that they can take on “Schwarzenegger,” German speakers… don’t. That’s just not how you say those sounds. One particular letter gets mangled.
It isn’t even an accent problem; you can say it correctly with a strong American accent. The American reinvention of “Schwarzenegger” represents a failure to understand how German sounds work, which is fine - hey, they’re “difficult” and “foreign” - but it is paired with total unearned confidence on the part of ALL Americans of ALL dialects that “of course we know how to say it. It’s a celebrity who was on the TV, he’s a governor, that’s how everyone says it.”
If you listen to Arnold saying HIS OWN NAME, which he does, you can tell that AMERICANS ARE NOT EVEN SAYING HIS NAME LIKE HE DOES. Even British people land a better attempt. It is a function of American cultural hegemony that Americans do not notice this. It is an inherently American view of the world to believe that a consistent, confident mispronunciation of someone’s name is a respectful, educated and correct handling.
(Tchaikovsky is interesting because it’s an Anglicisation of a French version of the spelling of Чайковский, which was possibly settled on because it was the easier way to get English speakers to perceive it. American English tried a different version in his own lifetime, as you can see below, but which would have led to Americans putting a “cow” in it.)
Again, it doesn’t cancel the slogan, the slogan is good-quality - but it shows how this is invisible to those who have not learned otherwise.
Outside of America, all Americans are perceived as American together, and Yanks join the ranks of English speakers. English speakers are famed around the world for having the same “bash and mangle it into something that sounds similar, and insist that it’s correct, because you don’t hear the difference” approach.
It will help in learning other languages to try. It will help a lot to take the loss with grace and accept correction!
Although the OP sort of accidentally implies that you “can’t” hear certain nuanced sounds - it is entirely possible to distinguish and perceive most nuanced sounds even in extremely nuanced languages, with intention and attention and training, especially with the guidance of a native speaker. Even if you can’t get it perfect it is still possible to improve and worthy to try!
IMO of the most fascinating ways for an English native speaker, especially an American one, to understand this is to watch how Mr Yang teaches Chinese students how to use American handling. “Soften up on the K sound” “throw in a little SpongeBob to it” you will suddenly hear things you probably weren’t ready to hear.
Here is a British person making a respectful attempt at Schwarzenegger, followed by Schwarzenegger saying it himself. One person has a British accent, and Schwarzenegger’s Austrian accent is considered distinctive to German speakers, but ideally, once you try to notice it, even if you are American, you should be able to hear what Americans are doing wrong.

One correction on that last point @elodieunderglass: Terry Wogan is Irish, not British, and although it's soft here, his accent is unquestionably Irish (although he did get British Citizenship in '05, he said all through his life his identity is Limerick, the city of his birth).
Honestly, the fact that Terry Wogan has an Irish accent adds another layer onto this, but I am very tired and my brain isn't firing on all cylinders so I'm really hopeful there'll be someone better qualified than me with the necessary bandwidth who is willing to go into it
There you go then! Thanks! I don’t know the presenter at all so I must regret that I didn’t know that, and grabbed it quite quickly trying to find a piece of Arnold saying his own name - allow me to demonstrate a graceful reception of correction!
Where the presenter tackles Arnold’s first syllable (“shvarts,” he does one brisk syllable, not the American “shwaaarz”. but you can also notice him tackling the “r” at the end as an “ah” sound, which is the way a lot of British people sidle up to it. But it’s also fairly close to how Arnold does it. The result is a more lifted and graceful sound and the vowels are lifted, not flat. So the presenter is either doing how RP presenters approach it, or is trying to follow Arnold. which is probably why it sounds like a handsome attempt, despite them both approaching it in a way that is probably odd-sounding to German German-speakers. At any rate: Americans get the ‘w’ wrong and add an extra syllable; the presenter here dodges both. Apologies for describing this badly, I’m not at all a linguist.)

















