I disagree with your claim that veganism and vegetarianism can't be backed by logical thinking. Producing meat requires significantly more natural resources (land area, water) and produces significantly more pollution (methane, ground contamination) than producing fruits and vegetables.
Here is an example comparing the amount of water needed to irrigate various crops compared to the amount needed to raise beef.
US Corn Production: 9 gallons water / lb corn
US Wheat Production: 14 gallons water / lb wheat
US Barley Production: 26 gallons water / lb barley
US Alfalfa Production: 31 gallons water / lb alfalfa
US Beef Production: 441 gallons water / lb beef
http://www.journalofanimalscience.org/content/71/4/818.full....
Global Spinach Production: 2 gallons water / lb spinach
Global Potato Production: 4 gallons water / lb potatos
Global Banana Production: 13 gallons water / lb bananas
Global Apple Production: 18 gallons water / lb apples
Global Lentil Production: 64 gallons water / lb lentils
Global Cashew Production: 121 gallons water / lb cashews
Global Almond Production: 252 gallons water / lb almonds
http://www.waterfootprint.org/Reports/Mekonnen-Hoekstra-2011...
I could look for more examples, but this took me about half an hour already, and I think it pains a rather compelling picture by itself. The difference would be less extreme when looking at pork and poultry, but there is still a stark contrast.
Here is an example comparing the amount of water needed to irrigate various crops compared to the amount needed to raise beef.
US Corn Production: 9 gallons water / lb corn
US Wheat Production: 14 gallons water / lb wheat
US Barley Production: 26 gallons water / lb barley
US Alfalfa Production: 31 gallons water / lb alfalfa
US Beef Production: 441 gallons water / lb beef
http://www.journalofanimalscience.org/content/71/4/818.full....
Global Spinach Production: 2 gallons water / lb spinach
Global Potato Production: 4 gallons water / lb potatos
Global Banana Production: 13 gallons water / lb bananas
Global Apple Production: 18 gallons water / lb apples
Global Lentil Production: 64 gallons water / lb lentils
Global Cashew Production: 121 gallons water / lb cashews
Global Almond Production: 252 gallons water / lb almonds
http://www.waterfootprint.org/Reports/Mekonnen-Hoekstra-2011...
I could look for more examples, but this took me about half an hour already, and I think it pains a rather compelling picture by itself. The difference would be less extreme when looking at pork and poultry, but there is still a stark contrast.