I think an important piece of the puzzle that I didn't see mentioned here is that most people, most of the time resolve their cognitive dissonance towards eating animals by not experiencing it. We put slaughterhouses in the countryside, remove any heads or hooves or skin from our butchers, hang out with friends who do the same, and often make it illegal to film how animals are treated.
Bastian and Loughnan talk about this as passive dissonance avoidance in "resolving the meat paradox" which is a summary of the literature you can read here: https://static1.squarespace.com/static/57d2f8668419c276f91f3b04/t/5846ac15579fb36bace325ee/1481026582391/resolving-the-meat-paradox.pdf
To anyone interested in this topic, the other great review (in my opinion) is "Toward a Psychology of Human-Animal Relations" https://static1.squarespace.com/static/57d2f8668419c276f91f3b04/t/5846af5f9f74567368763722/1481027424005/toward-a-psychology-of-human-animal-relations.pdf
I read this book, and one chapter in I thought it was too slow and anecdote heavy, and put it down. I persisted because of a friend and found about a third of the way in the quality of the advice and pace really picked up.
If anyone decides to read it, persevere!