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[Criminal Minds/Supernatural] What does the BAU think about Sam and Dean?

The FBI was hunting Sam and Dean a few years back. According to Agent Hendrickson, the Winchester brothers were assumed to be a pair of serial killers who were traveling the country murdering random people and desecrating graves for no reason.

Presumably, the BAU team had a hand in creating the "profile". Did they have any theories on the Winchesters' motivations? Who did they think was in charge? Did they have an explanation for the murders and grave defilements?
gpt
Dean and Sam Winchester.

Aliases: Innumerable. Pay attention to agents and individuals whose names are pop-culture references (e.g. Agent Stark amd Agent Banner).

Whereabouts: Unknown. Constantly on the move, they remain in one location for a very short period of time. Their locations have minimal connection to one another. Analysis found only slight connections, in the number of urban legends, and on previously unexplained crimes.

Associates: Deceased. A number of biker gangs have been connected with assisting the Winchesters over the years, attempts to trace these individuals has often been unsuccesful or hindered by unforeseen complications.

What We Know: The two brothers were raised by their father John Winchester, a vagrant, after the disappearence of their mother. Mary Winchester's (née Campbell) missing status was not reported until worries from the neighbours were investigated. John Winchester is still considered a person of interest for thr case.

Throughout their teenage and childhood years their location is hard to pin down. Various schools have children registered who bare a resemblance to Sam and Dean, and the few photos found confirm a few of these nodes. During these years it is believed they were raised by their father, but due to being neglected for long periods of time may have sought other father figures.

A split emerged in the family group when Sam attended college. From interviews with class mates and friends they all paint a picture of Sam as a quiet and kind individual, but noted he never talked about his family or past. At college he became involved with a woman named Jessica Moore (possible fiancé). Sam dropped out of college and is believed to have returned to his family. Moore is considered an unsolved homicide, with Sam Winchester the prime suspect.

Over the next decade we have intermittent reports and cases of unsolved homicides happening while the Winchesters are in the area. The cause of death in many of these cases has been ruled as accidental, but the statistical overlap of their presense and these deaths makes them persons of interest.

In the years of 2011 and 2012 their behaviour changed significantly. Multiple mass killings were committed by the brothers using machine guns. The locations were found to be sites of previous unsolved deaths that they had been in the vicinity of. 

Bodies matching known descriptions of the Winchesters were found in Ankeny, Iowa. This conflicts repeated sitings and photographic evidence of the brothers after this date. These bodies could be dupes used to attempt to remove police attention.

Psyche: Our analysis suggests that Dean is the enforcer of the brothers. Being the older brother he has sway over his brother, and we suspect that he uses the disappearence of Moore as leverage over Sam when they initially met to get Sam to join in his activities.

This doesn't negate Sam's agency. The act of Moore's disappearence, with the return to his familial structure, has lead Behavioural Analysts who worked in the 1980's to suggest a Satanic Cult. The idea, while challenged, may hold part truths. Moore may have been Sam's initiation to the family, or a way to apologise for leaving the group. What we know of the family structure and environment suggests that both Sam and Dean have been raised without normal morals.

At many crime scenes the brothers impersonate FBI (or other police forces) officers to get access to the crime scene. They also often continue to assist in the case, possibly to divert the case, or to revel in no one suspecting them. This is highly narcistic behaviour.

Both brothers exhibit psychopathy (through the string of deaths and corpse desecration that follows them across America), and Dean exhibits Machiavellianism through the leadership it is believed he has within the pair.

They are also linked to decades of fraud and identity theft. This furthers the evidence of psychopathy, showing an utter lack of empathy for their actions.

Prognosis: The brothers exhibit characteristics of the Dark Triad. The are suspected to be highly dangerous and armed at all times. The narcissism may be our advantage as they seem to believe they are on a greater journey, so seem unwilling to die. With suffecient planning we can prevent them from making the engagement planning.

Many years of unstable familial structures with a neglectful and amoral father has raised two brothers that seem to have mo cares for anyone but each other.