That was the crux of the matter, wasn't it? The right answer might give Harry a chance for a better future. A future where he did not have to look over his shoulder constantly. Where he was not on the run from a madman out to kill him every minute of every day. A selfish reason. The wrong answer might get him killed right here, right now. Was he willing to bow to a "Lord', who had seemed determined to destroy all muggles and "mudbloods" in the past? Of course not. But, he had to be honest, because a lie could jeopardize the sliver of progress they had already made.