Question

Psychologist have long struggled with how precisely to determine whether someone has apsychological disorder

Answer 1

That statement is true.

In general, they would categorize a person to have a psychological disorder if they display faulty pattern of thinking, feeling, or acting.
But all the things above are not a sure way to identify a disorder because the 'fault' could very much created by the tradition where that person grow up,not their psychological condition.