Mentioning his failure to kill Albus Dumbledore when they were in their sixth year at Hogwarts must have stung his pride. It was a well-known failure that he'd been taunted about for as long as Hermione could remember. Draco's name was synonymous with "coward" or "loser'. It all boiled down to the night he was unable to cast the spell to end his Headmaster's life. Maybe she shouldn't have been so surprised to hear that he'd never been able to follow through with another killing.