I do not believe that being a vegetarian reduces suffering. This is faulty understanding of buddhadhamma. Follow please:
It is taught in Theravada that kamma is the single-most factor determining the condition of rebirth (see abhidhamma for blow-by-blow description). Therefore if it is the fruiting of kamma of a being to be reborn in the animal womb, and in addition to be reborn as food, then it will be so. If an increase in vegetarianism reduces the number of animals killed in factory farms, then isn't it likely--according to the teachings--that the animal will be born in the wild, killed and eaten?
I believe so.
I saw on television a nature program showing a baby elephant that had been attacked and partially eaten by hyenas. It was beyond rescue; dying, and one of its eyes had been eaten out. It was a heart-wrenching and piteous sight to witness. Perhaps, I thought, this was the fruiting of a sentient being who had been "saved" from rebirth in a factory farm. I don't know, but I strongly suspect.
This world is hard, unsavory, often terrible.
Author of Redneck Buddhism: or Will You Reincarnate as Your Own Cousin?