Fire someone

As in to dismiss or discharge from employment, was originally American slang from the late 19th century but is now part of Standard English. It derives from the notion of discharging or firing a gun, which usage dates from the 1600s. Just as a bullet is fired or discharged from a gun, so is a person discharged from employment. To give someone the bullet means much the same thing and is a more modern 20th century version.