What does snuggling the pig do?
It's a running joke among the community that snuggling the pig before every mission increases your luck, but in reality snuggling the pig doesn't do anything except make the pig like you (which has no in-game effect). It's just something extra the developers added into the game for a little fun.
The reason the pig keeps running from you though is because it hates you. You really should snuggle it more often so it doesn't think you're a heartless pig hating robot.