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.
Turns out The Deathly Hallows did exist. It existed in Voldemort, Snape & Harry. Voldemort died for power. Snape died for love. Harry was the one who was willing to die. He greeted death like an old friend.