Man gets arrested for offending random woman by asking "Are you a mom?"

[Jehanne]

Here's an authoritative website:

False arrest, sometimes known as false imprisonment or wrongful arrest, occurs when someone wrongfully holds you against your will or takes you into custody. Both private persons and law enforcement agents can commit this crime when they act beyond or outside of the scope of their authority.

By contrast, suppose a police officer arrests someone because that person insulted the officer or did something the officer didn’t like. Insulting an officer is not a crime, and unless that officer has another reason to make an arrest, he is acting illegally. It’s possible, though unlikely, that a prosecutor could charge the officer with false arrest.

http://www.criminaldefenselawyer.com/false-arrest.cfm

And, so, basically, the cop would have to slip-up and tell someone that he arrested that guy to impress the woman or because he just did not like him.  But, getting handcuffed, is getting arrested, if only temporarily.  Getting charged with a crime means getting arrested, taken to jail, booked, fingerprinted, etc.