The phrase "fuck the police" originates with the
1998 NWA song, a response to a period of unrestrained violence and racism by the LAPD, an infamously problematic organization run by Daryl Gates, one of the single biggest contributors to police militarization and institutional racism in the country's history. It was a response to police malfeasance that most white or middle-class people in the country had zero exposure to, which only received any real attention years later during the Rodney King trial and subsequent riots, and which still continues to this day in an ongoing pattern of racially-biased actions by the LAPD.
So, I mean, it's gonna come off as inevitably hyperbolic when a white, middle-class person, shielded from most of the situation that originally prompted it, says it now, but it originates from a justified and legitimate anger at serious police misbehavior. An institution like the police should have to earn its reputation and immunity from this type of anger, and US police by and large have failed to do so.