This made me cry. Darn you crying Snape, and Harry with his mothers eyes. Snape had a complicated life if you read the books you would understand that he hates Harry through book but in book 7 he was friendly
But, actually, he chose a stag because it was large, powerful, and fast. It could survive a werewolf attack (assuming the worst case scenario happened). When the Marauders told Remus they were animagi.