"He who gives up meat-eating but does not alter his nature and thoughts, thinking to gain in spirituality, may flatter himself and perhaps make a fetish of his denial, but will certainly thereby make no spiritual progress." William Q Judge, 19th century
Many spiritual leaders, including my own guru, advocate a vegetarian diet in order to meditate well. It is often said that being vegetarian purifies the soul.
Some also say that eating meat causes us to ingest feelings of anger, fear and aggression. It makes sense that when an animal is killed the animal would have a lot of adrenaline pumping in it's veins, we ingest this adrenaline. Whilst I don't know of the modern scientific view of this concept, it is explained in Ayurvedic science as the qualities of sattva, raja and tamas, the latter of the two which are in meat.
For me it is a simple decision to live non-violently. To take of this bountiful planet, with thanks and respect, only what I need to sustain myself, causing as little impact on other beings in the process.
But, as I always stress, such sattva begins in the mind. It is about having a daily awareness of our universal consciousness, and doing what we can to support it. Without this consciousness, we can be vegetarian without any peace of mind.