Because pets need sunlight and fresh air, which vaults do not have.
Well, vaults do have artifical sunlight and something to clean the air. How else could humans live in the vaults without clean air (besides the ones that were designed to fail in that way)? They probably didn't allow pets anyways. Need room for lab ra---test sub----- humans.
The vaults have room and resources for about like 1/3000th of the country's population, they sure as hell won't let you bring a pet instead of another person. Besides there was that one vault, the one with the Panther..
Yeah but that Vault was only filled with 20 men and 10 women. They had the room to fit a panther, especily if the panther eats everyone.
They were probably eaten....