Billy was having dinner with his family last night. Billy's mother asked him if he could clear the table and wash the dishes because she needed to help his younger sister with her homework.
Billy replied, "Why don't you do it yourself?" with an angry tone. Billy's mother was furious because Billy had been mouthing off to her like this a lot recently.
Billy's best friend has a birthday party planned for Saturday. Billy is not allowed to go to the party because he mouthed off to his mother after dinner last night.
Sarah is very passionate about politics and likes to talk about it at her office. Politics can be a sensitive subject, but Sarah doesn't care if her opinions offend or hurt anyone. She mouths off about whatever she wants without respect for others. It is not surprising that Sarah is not very popular in the office.
to mouth off means to speak rudely and angrily to someone in authority. It can also mean to speak angrily or complain about something without thinking about your words and if they are offensive to those around you.
mouth off to someone - Billy mouthed off to his mother
mouth off about something - Sarah mouths off about politics
In example 1, Billy mouths off to his mother and she punishes him for it. In this context, to mouth off is used to show that Billy is speaking rudely and angrily to someone in authority who deserves respect.
In example 2, Sarah is described as a person who complains and talks angrily or negatively about things without thinking about the people around her.
This idiom can be found in the LSI textbook Speaking Transitions. This book is used at LSI schools in the level 4 Listening/Speaking classes. For more information, please visit: www.languagesystems.com