Islam never had a monopoly on religious beheading. And religion never had a monopoly on beheading. People simply kill each other and it is a side effect of human nature. You can apply whatever label you want to either society and they will still compete over resources and ideas. They will still dehumanize the other and unite their own dominion under a common banner of hatred towards the other. This is how society functions on a basic level people, it is the basis of government having any longevity. No one has a monopoly on society, and the whole reason that people do things like that on a large scale is because people organize with one another. They become an entirely different animal when they are subjected to group pressures and indoctrinated from birth.
Critical thinking, on the other hand, is both the enemy and the gadfly of society. It is the whip that forces society into progressing inch by inch and many times society lashes back aggressively, even to the point of marked societal regression. Before society, men and women used to have comparable influence, and although conditions could be harsh life was simple and there was not much to consider. People simply enjoyed the company of others. Yet still there was violence between families and clans, it was merely less prevalent.
Violence is symptomatic of basically any association between people because our animal nature will always rebel against critical thinking, as the amygdala, medula, and pons, will always react more frantically to pressure than the hippocampus or prefrontal cortex. In the regions of the brain associated with critical thinking, there is a good deal less stimulation from serotonin and more euphoric chemicals like cannabinoids. So on a basic scientific level it is impossible for terrible violence not to happen, as certain functions of the brain are more prevalently used over others when people are examined as a group. Religion or no religion the amygdala and medula will always incite violence and terror. This was plainly evident amongst the atheistic regimes of the 20th century.
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There is no wealth like knowledge, no poverty like ignorance.
Nahj ul-Balāgha by Ali bin Abu-Talib