Beyond its literal meaning, it is used with a specific sense by the toilet flush button, leading to the figurative sense "definitively get rid of what no longer serves", as excrement is removed. See "Throw the Chain" .
PRESSING THE BUTTON in literary form consists of pressing on a contact (to activate or deactivate something). Figuratively, provoke an incident: John pressed the button with that phrase and the fight did not wait. There were 3 hospitalized.