During The Dark Knight, The Joker visits Dent in the hospital to shift the blame off himself. But why would Dent believe him?
The Joker is undoubtedly responsible for Rachel's death.
Why would he just let him go?
The joker says he didn't make the plan. It sounds a terrible lie. Who else would plan on using explosives to get them killed?
At the time of his conversation with the Joker, Dent is seething with rage about Rachel's death. He's not really thinking pragmatically.
Don't forget that the Joker swapped Harvey and Rachel's locations when he spilled the beans. He expected that Batman would rescue one, and send the police to rescue the other.
Joker also correctly predicted that Batman would try to rescue Rachel (he saw Batman dive out of a window to save her before, it makes sense that he'll try to save her again).
Harvey resents Batman for saving him and not Rachel. It's somewhat expected that Batman has a better shot at saving someone compared to the police, and since Harvey wants Rachel to be saved instead of him, Harvey resents Batman for not trying to save Rachel instead of him (Harvey does not know that the locations were swapped).
Notice that while Harvey still is in the hospital, no one has told him about the locations having been swapped. It would only make Harvey feel even worse (knowing that Rachel could have been the one that was saved, but died anyway). The Joker manages to have his conversation with Harvey before he is aware of the swapped positions.
Also keep in mind that Rachel and Harvey were part of this game because corrupt police officers captured them. Harvey is well aware of this, since he remembers being taken, and likely has already heard that the same happened to Rachel.
Joker's argument to Harvey relies on a few key points, some of which are implicit (relying on what Harvey already thinks, without the Joker explicitly having to state it). I'm describing these from the point of view of the Joker, based on what Harvey thinks is the truth:
The emphasis is on the people who Harvey would likely consider equally responsible for Rachel's death. Notice how Joker's arguments mostly put the blame on the corrupt and fallibly good guys. Harvey is looking for a guilty party to convict, and the Joker is subtly offering the police and Batman as the biggest perpetrators of the injustice of Rachel's death.
These are subtle points, mostly driven by what Harvey already knows, and slightly tweaked by the Joker's argument that he's not the only evil.
Harvey realizes that the Joker is not the sole reason why Rachel died. If anything, the fact that Harvey survived proves to Harvey that Rachel could have survived this too.
But she didn't. Because they (police+Batman) failed to save her. They contributed to Rachel's death as much as the Joker did.
That's what Harvey takes away from his conversation with the Joker.
During the Joker and Harvey's conversation, Two-Face is born. I won't call him Harvey anymore, because Two-Face operates under a different belief than Harvey Dent did.
The Joker is already convinced that he has swayed Two-Face, because he gets Two-Face to aim a gun at him.
However, the Joker was not aware of Two-Face's "coin flip" method. The coin flip is Two-Face's way of punishing the guilty. He does not outright kill everyone who was involved. He gives everyone a 50/50 shot.
This is the core of the answer:
Dent believes the Joker that others are also responsible. Dent does not believe that the Joker is in no way responsible. Dent forces the Joker's life to rely on "the coin flip", which proves that Dent considers the Joker to be guilty.
Two-Face considers everyone (who ends up getting a coin flip from him) to be part of the same conspiracy that killed Rachel. Whether they are part of it intentionally (Joker, the corrupt cops, Maroni) or unintentionally (Gordon, Batman) doesn't really matter to Two-Face.
Although we do not see Joker's 50/50 shot, we see Harvey flip the coin while still having a gun to the Joker's head, and we see the Joker still alive in a following scene. Logically, the Joker must have had a lucky coin flip.
The Joker isn't lying though when he talks about him not having a "plan" he means that he has no grand goal - he is merely acting as an agent of chaos and disrupting the plans and schemes of others. By doing so he's trying to demonstrate what he sees as the futility of living to such plans.
The outcome of this is that Dent sees that whatever the desires of himself or the police or even Batman ultimately whether he or Rachel died came down to what was essentially a coin toss and if the single most crucial moment in his life (as he sees it) came down to nothing more than a coin toss then why not let embrace it fully. Which is why abides by the coin flip outcome as to whether to kill the Joker or not. All his efforts to control his life and those around him for the better have done nothing to prevent him reaching this moment where he has nothing but overwhelming physical and emotional pain so why even try? It's all just a coin toss anyway!
Joker tells Dent about "Schemers" which are true evil as they lay out the plans for society especially when human life is expendable. He makes his point by saying that society does not panic when the expected people get killed such as a gangbanger or soldiers. Thus Joker has turned Dent against the schemers who viewed his and Rachel's lives as expendable, namely Gordon for choosing to work with corrupt cops, the corrupt cops in Gordon's unit who kidnapped them, and mob boss Maroni who hired the Joker and Joker advises Dent to break away from the legal justice system that failed him and instead turns to chaos which is the only fair justice in society.
