There are some previous CR threads on this topic, in case you want to see what I and several other of these posters said previously.
Rabbi Dovid Sears has a book (The Vision of Eden) explaining rabbinic opinions for and against vegetarianism. A draft of the book is available for free online. It’s very interesting — highly recommended. Many famous rabbis have either been vegetarians or praised vegetarianism (the Sdei Chemed is in the latter category, for example).
While some hold that eating meat is required on Shabbos or Yom Tov, the majority opinion is that it is not required. The head of the Jewish Vegetarians of North America is an Orthodox Jew.
In my view the main issue with vegetarianism and veganism is hashkafic. Despite what some people claim, there is nothing wrong with being a vegetarian because you want to minimize animal suffering. It is an aveira to cause unnecessary suffering to animals, and modern animal production methods certainly do that, beyond any doubt. So being vegetarian, or near-vegetarian (eating meat only on Shabbos and Yom Tov, for example, as Rabbi Lazer Brody recently recommended for health reasons), is way to be machmir about tzaar baalei chayim.
What is problematic is the animal rights belief that animals have the right not to be eaten, or that we have an obligation not to eat them or use their milk or eggs at all. By that logic, the korbanos would be immoral, and so would tallesim and tefillin and sifrei Torah, c”v’s. You can certainly be a vegetarian for animal welfare reasons yet not think it is inherently wrong to ever eat or use animals.
Another hashkafic problem is that vegetarianism, and especially veganism, has kind of become its own religion. Many vegans are very militant and associate mainly with other vegans. Thus it is hashkafically dangerous to become vegan, as one may become infected with heretical notions and believe in an all-encompassing worldview that replaces Yiddishkeit in your life.
Realistically, vegetarians are never going to convince the whole world. And eating meat occasionally is not that different from becoming completely vegetarian, in terms of its impact on the market. So in my view the best way to reduce animal suffering without endangering your overall avodas Hashem is to be a moderate vegetarian or near-vegetarian (eating meat, fish, dairy or eggs at least in small amounts or on occasion) while supporting organizations (animal welfare-oriented, not animal rights) that work toward improving the conditions in modern animal agriculture.
As an aside, one halachic advantange to being a vegetarian (even a lacto-ovo-pesco vegetarian) is that if your kitchen is only dairy, you don’t have to worry about meat/milk mistakes.