Use this expression to talk about something that you don't want.
You tell someone "The last thing I want is for..." when you want to make sure that they don't misunderstand you. In the example above, the speaker is worried that the daughter thinks that she can't talk about her love life with her parents.
You can also say "The last thing I want is to (do something):
The last thing I want is to cause an argument on your birthday, but this is a serious problem.