YES! But uh...it depends on who you ask.
There is a halachic basis for the rabbis who declare you must eat meat on Shabbat. (Though even they will admit there was a great rabbi-whose name I forget-who was vegetarian every day but Shabbat.) I find most of these rabbis tend to be far to the "right" in the orthodox community.
My understanding is that the source for this is that the Talmud says one is required to be happy on Shabbat by eating meat and drinking wine. On the other hand, other rabbis conclude that the list was given to be merely an example of the things that could make you happy. And that if eating meat would make you unhappy, it would actually be a mitzvah for you to avoid eating it on Shabbat.
All that said, I know of at least one beit din that requires vegetarian converts to vow they will eat meat on Shabbat and will accept no other interpretation. So if you're a vegetarian or vegan, I suggest throwing it out there to your rabbis as early as possible to see how they react. There is definitely a machloket, and if you need to change to another beit din, so be it. Otherwise, be prepared to accept their ruling (and maybe later figure out how you can choose to follow a new ruling).
And now for your enjoyment, one of the best "stuff people say" videos I've seen.
Disclaimer: While I am not a vegetarian or vegan, I was a vegetarian for a relatively short time in the past. (And I'm primarily a vegetarian because I'm lazy.) The comments in this video are not limited to Jews. I can personally attest to the French people's similar confusion and stubborn insistence that chicken isn't really meat. (Most Americans are too politically correct and have been exposed to a great deal more vegetarianism than most of the world!)