There is more on this subject wihin scripture than I think most realise. Also the Scriptures are more interlinked than seems to be appreciated. The Old Testament law is discarded in the usual conversation of this subject, and reference is made to some interpretation of the New Testament to do this. But is this accurate?
D&C 49:18 states that whoever forbids a person from abstaining from meat (that man shouldn't eat it) is not ordained of God. A clear statement that God, firstly, regards it possible (at least) to be vegetarian. This, secondly, makes it obvious that he is not opposed to it at all. So why even bother mentioning it? It is fairly heavy in its way. He is saying a person commanding against vegetarianism is not from him.
D&c 89 contains the obvious statements. But how many examine them relative to past instruction? Note verses 14 and 15, "...and all wild animals that run or creep on the earth; And these hath God made for the use of man only in times of famine and excess of hunger." So does this mean we can eat domesticated pigs but not wild ones? As we domesticate dogs and cats can we eat them, also? God gave instruction of what he was talking about long ago. He had Moses write it down. No pigs, dogs, cats, camels, shark, dolphins, squid, octopus, crabs, crayfish, mussels, oisters, eagles, ants, cockroaches and so on. Because the Israelites of the time were so spiritually backward he made it a commandment, so at least some would follow it.
Have you questioned yourself as to why God would ask such a thing? It is because the meat of these things is worse than the meat of the other animals. Isn't that plain?
Now God has made it a request, not a commandment. But don't the scriptures tell us that it is a slothful and not a wise servant that needs to be commanded in all things (D&C 58:26). In regard meat he has said that it is pleasing to him that it shouldn't be eaten, unless it is cold or there is a famine.
As personal advice from personal inspiration let me advise anyone wishing to stop eating meat that they should break off it slowly. Quit all the really bad stuff mentioned above immediately. Then break off red meats, and just eat fish and chicken. Then break off the chicken. Then off the fish eventually. This should be done over a couple of years.