As per Jainism, Milk is considered as Vegetarian only not as Non-Vegetarian.
Milk is veg as its does not contain the cells which u find in non-veg. Milk is not meat. Extracting milk, does not pain or trouble cows /buffaloes. It's a satvik diet having beneficial effect on mind and body. So there is no harm in consuming milk. Of course using injections on animals to increase milk, denying milk to calves is a sin.
Those who get into this debate of milk being vegetarian or not should first understand that the reason of banning certain foods for civilized humans is 2 folds:
- It harms your own mind/body
- It troubles/kills/ pains other living beings.
Anything that satisfies either of above 2 criteria, is Abhakshya food (Non-Eatable). Everything else is Bhakshya (Eatable).