Put yourself in the shoes of the characters, who know a fraction of what the audience does. More than that, remember that they're people and not robots, and consider the context the movie spends like two hours giving us:
The public, and the police, are scared and angry. The only things they know for sure is that Batman is a violent vigilante, and that he refused to show himself and let someone die.
Dent tries to talk people down, encourage them to be rational and reasonable, and one of the officers in the crowd yells "NO MORE DEAD COPS!" and people cheer.
So what are they going to think when the DA, who they adore, turns up dead, and a hero cop says he saw Batman do it? What are they going to be primed to believe? Is it going to be that one of their heroes is lying, and that the other snapped and embraced chaotic nihilism, or is it going to be that the weirdo coward in the bat costume beating the crap out of people was responsible? You know, the second weirdo in as many weeks to show up in a bizarre costume and start murdering?
The public, and the police, are scared and angry. The only things they know for sure is that Batman is a violent vigilante, and that he refused to show himself and let someone die.
Dent tries to talk people down, encourage them to be rational and reasonable, and one of the officers in the crowd yells "NO MORE DEAD COPS!" and people cheer.
So what are they going to think when the DA, who they adore, turns up dead, and a hero cop says he saw Batman do it? What are they going to be primed to believe? Is it going to be that one of their heroes is lying, and that the other snapped and embraced chaotic nihilism, or is it going to be that the weirdo coward in the bat costume beating the crap out of people was responsible? You know, the second weirdo in as many weeks to show up in a bizarre costume and start murdering?