So my question is why does Harley go to black gate at the end even tho she is mentally deranged. John gets to go to Arkham.
I don´t really think that she is as crazy as other Arkham inmates. This Harley seems to be more "sane" than the classical one, at least when you compare her to other Batman villains. I think she doesn´t have more mental problems that Penguin, for example.
Are they horrible people that kill withour hesitation? Sure, but they are more stable than Harvey or John.
The closing of state hospitals in the 1970s and 1980s led to the containment of mentally ill people in correctional facilities. Today our jails and state prisons contain an estimated 356,000 inmates with serious mental illness, while only about 35,000 people with serious mental illness are being treated in state hospitals. When a mentally ill person comes into contact with the criminal justice system, the decision about whether that person belongs in jail or in the hospital is rarely a clinical one. Instead, it’s made by police officers, prosecutors, and judges.
Harvey Dent also has the opportunity to go to either Arkham or Blackgate. Limited space, limited funding, welcome to the revolving door of a not so fictional system.
Her mental illness hasn't set in yet. The genetic illness her father has.