The fundamental problem is not people's flawed logic, but the psychological diagnostic tests. Psychologists broadly categorize most disorders because they cannot find a reliable symptom that also acts as evidence of a disorder. That is, there is no symptom that definitively allows psychologists to say "Patient exhibits Symptom X. Therefore, patient has Disorder Y."
Contrast this to "biological" diseases like viruses or cancers. They exhibit physical evidence as symptoms. Doctors can detect the physical presence of a virus or a cancer. The evidence they find serves both as a symptom and evidence of their diagnosis. Thus, medical doctors can precisely define diseases by their symptoms.
Unfortunately, psychologists are not afforded such luxury. Yet many of them act as though they are. This is how we end up with severe misdiagnoses. We need to be aware as a society of how this affects us.