In the Shree Swaminarayan Gadi Granth, Jeevanpran Swamibapa narrates an episode in the jeevan leela of the supreme Lord Swaminarayan, which directs us to the answer the question about vegetarianism.
During Lord Swaminarayan's forest expedition, He arrived at Jagnathpuri. Here, there lived a large community of demons disguised as sages. One day, one of these sages said to the Lord, "Pick this green plant." The Lord refused to do this saying that the plant was a living entity and by plucking the plant, it would cause it pain. The sage was angered by the Lord's refusal, and this sparked off a huge battle where thousands of these demons were slain. The point that the Lord demonstrated was that it was not necessary to pluck the plant. Unnecessary killing of plants is a sin, just as is the killing of animals.
The Lord has made 4 types of creatures.
Each of these requires sustenance to survive and this can only be met from the other types of creature. A lion requires flesh to survive. God has built the lion with claws and teeth appropriate for this purpose. Therefore, it is not a sin for a lion to kill another creature and eat its meat. But, a lion will only kill enough for it to eat. It will not kill unnecessarily. Our forefathers may have eaten meat. But they realised that man can survive on vegetation alone, and between meat and plant matter, the latter was less sinful. The ancient rushi munis thus weighed up the options and decided that man should eat plant matter.
Cutting nails or hair is different from cutting off a finger or another limb. They are all parts of our body, but there is a distinction. In the same way, there remains a distinction between killing an animal and a plant for food, even though they both have life. Having said this, needless killing of plant matter is just as much a sin as killing an animal.
Thus, the eating of plants by humans is allowed, because it is necessary for its survival. And, if you then use the energy derived from that plant in the worship of God, then in fact you are giving salvation to those plants, because the plant has been of use in worshipping God. However, if you do not use the energy derived from the plants in worshipping God, then indeed you are committing a sin by the killing and eating of the vegetation.
The Lord has commanded that water should be filtered before drinking. This is to remove any organisms or bacteria so that we may not consume these, and thus cause their unnecessary killing. God had further commanded that if a pot of water has been left for over 24 hours, it must be re-filtered before use. This is to remove any organisms that may have grown over that period. Again, Lord Swaminarayan has given further credence to the ideology that unnecessary killing should be avoided.
The health experts today advise us that a vegetarian diet is generally a healthier diet. Our forefathers were correct in their advice.
As a final point, humans are indeed the biggest sinners in the universe. It is a fact that every soul leaves each life with more sins than when it entered that body. But as it says in the Bhagawat Gita,
The true and unadulterated commands of Lord Swaminarayan (dharma) are eternally alive at Shree Swaminarayan Gadi. By obeying the wishes and commands of His Divine Holiness Acharya Swamishree, through whom Lord SwaminarayanBapa Swamibapa gives darshan today, we will become relinquished of all our mortal sins and attain the supreme bliss of the Lord's murti.