I think there are a couple of problems with being 'friends' with coppers.
The general members of the public they meet are, lets face it, scum. They are meeting the Jeremy Kyle lot day in, day out. The only decent people they tend to mix with are other coppers, therefore they easily get sucked in to the 'culture' of the job. The job become a life style for them, not like most of the rest of us who do a job and then switch off after work. This can make them seem a bit boring for the rest of us as they are less up for a laugh, generally don't muck around etc.
They also (like teachers) boss people around all day. This can on occasions cause people to become arrogant.
This is not true in all cases and I am sure there are plenty of exceptions to the rule but as a generalisation, I would say it is pretty true.