If you insult someone in public, they can ignore you, insult you back, or react with violence. If the person you are insulting is a cop, they can also arrest you, even though the charges are almost always thrown out of court. The Marshall Project looks at six cases in which people hurt a cop's feelings and were arrested for it.
The middle finger
Case: State of Connecticut v. Anonymous (Superior Court of Connecticut, 1977)
Summary: A school bus, taking high school students home, stopped at an intersection. A police cruiser stopped behind the bus. A Connecticut court describes what happened next: "The defendant (a student in the back of the bus) wiped the condensation off the rear window of the bus and, upon seeing the trooper, waved a school chum over to him and then proceeded to make a gesture toward the trooper in which the middle finger of the defendant's right hand was held in an upright position with the palm of the hand toward the defendant." The trooper hit his siren, boarded the bus, and arrested the student, who was charged with and convicted of making an obscene gesture.
Finding: On appeal, a court threw out the conviction, writing: "To be obscene the expression must be, in a significant way, erotic. … It can hardly be said that the finger gesture is likely to arouse sexual desire. The more likely response is anger."