What were the primary reasons for different livestock consumption habits of countries and cultures?
Id'say availability, like others have commented on.

If you have access to sea, seafood is an easy choice.

You cannot keep cattle high up in the mountains, that's why goats and sheep are more popular in e.g., Greece, where there are no plains for cattle to graze on.

Chickens and doves are easy to keep and were cheaper than pigs or cows.

Pigs are omnivores. On the one hand, they are happy in forest regions eating acorns (which cows wouldn't like). Pigs also eat kitchen trash like potato peel and leftovers. On the other hand pigs compete with humans for food (potatos, fruit).

Other animals were primarily work animals (dogs to guard, cats to catch mice, horses to pull carts and ploughs) and were hence not eaten (there are exemptions to this rule like Sauerbraten which was made from horse meat of horses that were too old to be used as work animals).