In secular circles, the top reasons cited for embracing a vegetarian diet are avoiding cruelty to animals, improving your health, and helping the environment. All three of these correspond to important Jewish values.
Jews should not inflict unnecessary pain and suffering on animals (tsa’ar ba’alei chayim). According to the Shulchan Aruch (Code of Jewish Law), “It is forbidden, according to the law of the Torah, to inflict pain upon any living creature. On the contrary, it is our duty to relieve the pain of any creature ….”
According to the principle of pikuach nefesh, it’s important to stay healthy. Says Maimonides, “Since maintaining a healthy and sound body is among the ways of G-d—for one cannot understand or have any knowledge of the Creator if he is ill—therefore one must avoid that which harms the body and accustom oneself to that which is helpful and helps the body become stronger.”
According to the principle of bal tashchit, we should be good stewards of the environment and not waste resources.