Why make Peter Pettigrew the Secret-Keeper?

Quote	Source
"James Potter told Dumbledore that Black would die rather than tell where they were, that Black was planning to go into hiding himself ... and yet, Dumbledore remained worried. I remember him offering to be the Potters' Secret-Keeper himself." "He suspected Black?" gasped Madam Rosmerta. "He was sure that somebody close to the Potters had been keeping You-Know-Who informed of their movements," said Professor McGonagall darkly. "Indeed, he had suspected for some time that someone on our side had turned traitor and was passing a lot of information to You-Know-Who."	Book 3, Page 205 Prisoner of Azkaban, Chapter 10, "The Marauder's Map"
"But then...," Lupin muttered, staring at Black so intently it seemed he was trying to read his mind, "... why hasn't he shown himself before now? Unless" - Lupin's eyes suddenly widened, as though he was seeing something beyond Black, something one of the rest could see, "-unless he was the one ... unless you switched ... without telling me? Very slowly, his sunken gaze never leaving Lupin's face, Black nodded.	Book 3, Page 344 Prisoner of Azkaban, Chapter 17, "Cat, Rat and Dog"
"I persuaded Lily and James to change to Peter at the last moment, persuaded them to use him as Secret-Keeper instead of me. ... I'm to blame, I know it."	Book 3, Page 365 Prisoner of Azkaban, Chapter 19, "The Servant of Lord Voldemort"
"Remus!" Pettigrew squeaked, turning to Lupin instead, writhing imploringly in front of him. "You don't believe this ... wouldn't Sirius have told you they'd changed the plan?" "Not if he thought I was the spy, Peter," said Lupin. "I assume that's why you didn't tell me, Sirius?" he said casually over Pettigrew's head. "Forgive me, Remus," said Black. "Not at all, Padfoot, old friend," said Lupin, who was now rolling up his sleeves. "And will you, in turn, forgive me for believing you were the spy?" "Of course," said Black, ...	Book 3, Page 373 Prisoner of Azkaban, Chapter 19, "The Servant of Lord Voldemort"
"Lily and James only made you Secret-Keeper because I suggested it," Black hissed, so venomously that Pettigrew took a step backward. "I thought it was the perfect plan ... a bluff. ... Voldemort would be sure to come after me, would never dream they'd use a weak talentless thing like you."	Book 3, Page 369 Prisoner of Azkaban, Chapter 19, "The Servant of Lord Voldemort" Spoken by Snape.
PONDER THIS
"I myself gave evidence to the Ministry that Sirius had been the Potters' Secret Keeper."	Book 3, Page 392 Prisoner of Azkaban, Chapter 21, "Hermione's Secret" Spoken by Dumbledore.
"You'd have died like your father, too arrogant to believe you might be mistaken in Black -"	Book 3, Page 361 Prisoner of Azkaban, Chapter 19, "The Servant of Lord Voldemort" Spoken by Snape.