Why Is Arthur Shelby Crazy?

Arthur's biggest problem is not learning from his past mistakes. He opens himself up to emotional trauma and betrayal, which is something he cannot afford to do in his line of business. For example, when his not-so-caring father returned to Birmingham, Arthur wanted to impress him for no apparent reason.

What does Arthur Shelby suffer from?

One of the major symptoms of PTSD is "recurrent, unwanted distressing memories or dreams of the traumatic event"[1]. A number of characters in Peaky Blinders appear to suffer from it, the most notable ones being Thomas Shelby, Arthur Shelby Jr., and Danny Whizz-Bang.

What problem does Arthur have in Peaky Blinders?

He suffers from ptsd and mental instability. During childhood, he was probably ignored by his father and received severe neglect. He grew up with gangsters and cut throats, probably always feared in school.