In my life I have only known three servicing police officers, two I played football with. All three were arrogant and one was an out and out bully. Not represent sample I'd agree but it's always made me wonder whether these qualities were actively sort after as part of the recruitment process or became inbred as part of their training, or both, or neither and that I simply encountered outliers.
The ones I've known personally have been decent people and weren't arrogant in anyway. One was a Police firearms Officer and I don't think I've met a quieter bloke than him.
I suspect (but have nothing to back it up) that it attracts plenty of the arrogant type and some change to that based on what they face on a regular basis.