Peter Pettigrew doesn't want to be a cliché; he doesn't want to be that guy who resents his best friends' girlfriend. He doesn't want to only be known as 'the boy who adored Potter,' he doesn't want to be that guy whose best friends are all far more witty and charming than he, he doesn't want to hold down a boring desk job at the Ministry of Magic while his friends fight in the war full time. He wants to be remembered as someone who changed history. So when Bellatrix Black offers him protection and glory, he does not hesitate.
