Leonato and his brother challenge Don Pedro and Claudio to a duel. Why?(Act 5)

Leonato challenges Claudio to a duel on the grounds that he killed Hero through his accusation and wrongly harmed Leonato's reputation. Antonio steps forward and supports Leonato by challenging Claudio as well. Leonato tries to stop him, but Antonio continues hurling insults at Claudio and Don Pedro for the way they treated Hero. Don Pedro refuses to accept the challenge, telling them that Hero, "was charged with nothing / But what was true and very full of proof"