The mitsvah of eating meat

Dear rabbi, I was told that on Yom Tov, it is a mitzvah to eat meat. As a vegetarian, I find it very hard to believe that eating meat is a mitzvah, and I don’t think it's ethical.

Thank you for your query
This is a very loaded subject with lots of different opinions and ideals, so it is important to be clear about the Torah and Halachic perspective on this issue.
It is important to note that there is no nation or religion that looks after the well-being of animals like the Jewish nation does. There is even a prohibition called tza'ar ba'alei Chayim that one may not cause any undue distress to animals. There are opinions in Halacha that this is even a Biblical Prohibition as written in the Kitzur Shulchan Aruch, (Siman 191) “It is forbidden by the Torah to cause pain to any living creature, and on the contrary, one is obligated to save any living creature from suffering, even if it is ownerless or belongs to a non-Jew”.
It is even stated in Halacha (Siman 116,6) that if one sits down to eat and then remembers he hasn’t yet fed his animals, he must first feed his animals, and only then may he sit to eat. This is learned from the verse: ונתתי עשב בשדך לבהמתך ואכלת ושבעת " And I will give grass in your field for your cattle, and you shall eat and be satisfied."
Yet we find in the Torah that one may slaughter and eat the meat of Kosher animals, which are listed in Leviticus, Chapter 11, and Deuteronomy, Chapter 14., and as you correctly wrote it is at times even a mitzvah to eat meat like on Jewish festivals as brought in the Mishnah Berurah (siman 529, 11)
We also find that in the times of the Bais Hamikdash Animals were brought as sacrifices and when the the Kohanim would eat from the meat of the sacrifice it would bring atonement for the owner. As it is brought in the Sifra, Shemini, Parsha 1, Chapter 2, כהנים אוכלים ובעלים מתכפרים.
So we need to understand the balance on the one hand, there is a prohibition of Tza'ar Ba'alei Chayim as was mentioned earlier, and on the other hand, we find that one may slaughter an animal and eat the meat, which is considered a mitzvah and can even bring about atonement.
The reason is that in Judaism we appreciate that a human who serves Hashem is not just another link in the food chain but rather through eating one elevates the food to a spiritual level.
The Maharal elaborates that in the creation of the world, there are four categories :
דומם - earth and rocks
צומח - like grass and vegetation
חי - animals
מדבר - humans
When one eats meat he is elevating all the categories of the physical world since the cow which is חי ate grass which isצומח and the grass grew from the ground which is דומםand now all these parts of creation become a part of the human and so when he will now prey to Hashem and praise Hashem and do mitzvot, in essence all these become a part of him and a part of his service to Hashem.
The Ramban in his Sefer Igrot Kodesh chapter 4 explains it further that it says in Tehilim (145,9)
טוֹב ה' לַכֹּל וְרַחֲמָיו עַל כָּל מַעֲשָׂיו – “Hashem is good to all, and His mercies are over all His works”
Explains the Ramban that before Hashem created the animals he asked the animals “Would you want to be part of man and be able to praise me and have a part of doing mitzvot?” and they answered, “we wish!” Hashem then initiated the mitsvah of Shechitah and then by eating the meat of the animals, they become a part of the one who is serving and praising Hashem.
We see from the above that eating meat has a lot of depth and holiness and is an opportunity to do kindness to the animal.
We can further appreciate the holiness of eating as brought in the Sefer Mesilat yesharim chapter 26:
ספר מסילת ישרים פרק כו
הצדיקים הן הן המרכבה, כי השכינה שורה עליהם כמו שהיתה שורה במקדש, ומעתה המאכל שהם אוכלים הוא כקרבן שעולה על גבי האישים, כי ודאי הוא שיהיה נחשב לעילוי גדול אל אותם הדברים שהיו עולים על גבי המזבח כיון שהיו נקרבים לפני השכינה, וכל כך יתרון היה להם בזה, עד שהיה כל מינם מתברך בכל העולם, וכמאמרם ז"ל במדרש - כן המאכל והמשתה שהאיש הקדוש אוכל, עילוי הוא למאכל ההוא ולמשתה ההוא, וכאילו נקרב על גבי המזבח ממש.

The righteous are conduits for the holy Shechinah like as if they were the bais hamikdosh so when they eat it is considered like a sacrifice on the alter and like when bringing a sacrifice it was a great elevation to those animals since they were being brough as a sacrifice in the presence of the Shechinah and not only is it a blessing for this animals but it also would bring blessing to all the type of animals throughout the world. Same too when a holy person eats it is like it was offered on the altar.
I hope I was able to enlighten you on the Jewish perspective on eating meat and help you appreciate its holiness.
Wishing you well.

1. Kitzur Shulchan Aruch, Siman 191
2. Halacha, Siman 116,6
3. Leviticus, Chapter 11, and Deuteronomy, Chapter 14
4. Mishnah Berurah, Siman 529, 11
5. Sifra, Shemini, Parsha 1, Chapter 2
6. The Maharal
7. Ramban, Sefer Igrot Kodesh, Chapter 4
8. Mesilat Yesharim, Chapter 26