God does not support vegetarianism for a good reason. It is important that we value animals in our life because they spread seeds, help keep the land fertile and recycle and clear vegetation and because they are a protection in times of famine or need. He did command that we should not shed blood when we had no need. He is very supportive of fruits and vegetables and things we do not have to kill to eat.
Many people in the Climate Change circles are trying to limit animals without realizing the danger that would be to the planet.
God commanded that some animals are clean for eating and others are not in Leviticus 11. He commanded the eating of lamb for Passover and for bringing animals for sacrifice and enjoying in His presence. (I guess He likes tailgate parties too.) He likes to see His people rejoice and to share with others. Animals make a great gift to give to the poor or as wedding presents etc. because they keep on giving.
I really enjoy many vegetarian dishes especially when I can get what other cultures have enjoyed. You are right about the health benefits to limiting meats. It is reported that most preventable deaths could have been saved by not consuming meats. Meats produced for eating are fed grains and unnatural diets for them and it changes the ph of our blood and their blood making us both susceptable to diseases. (Dr DC Jarvis). If the animals were left to feed naturally it would release enough grain to feed the starving people of the world. We must do all things according to God's word. He made the world and He knows how it works together for the benefit of all.