The chest mirrors your argument back, and you go and kill yourself. But you fail in the attempt.
(David Monroe is one of the aliases of the same guy who also has Lord Voldemort as another alias in HP:MoR. Super smart, lots of experience, and utterly without scruples, willing to put up with all sorts of stuff for a long-term goal.)
I ask the chest how it would solve Harry's dilemma of having 30+ death eaters pointing wands at him, with Voldemort wanting a response to his challenge.
(Yes, that's trying to encourage you to read a great fanfic/book)