to not understand something correctly► misunderstand to think that someone means one thing when in fact they mean something else: · I think she misunderstood you.· I'm sorry, I must have misunderstood.· According to Bennett, you misunderstood the reason you were dropped from the list.
► misunderstanding a problem caused when someone does not understand something correctly: · There seems to have been a misunderstanding. I didn't order steak.· Cultural differences between people from different countries can sometimes lead to misunderstandings.
► misinterpret to not understand the true meaning of someone's actions or words, so that you believe something that is not in fact true: · Your friendliness could easily be misinterpreted.· A lot of people misinterpreted what I was saying, and have called me a racist.
► misread to wrongly believe that someone's actions show that they have a particular opinion or feeling: · Unfortunately, we misread the situation and lost a lot of sales.· The intelligence community was criticized for misreading Iraq's intentions.
► miss the point if you miss the point , you think you understand what someone says or what is important about a situation, but in fact you are wrong: · I soon realised that he had completely missed the point.· He's so caught up in the rules that he's missing the point of the game, which is just to have fun.
► take something the wrong way to be offended or upset by a remark that was not intended to offend or upset you, because you understood it wrongly: · Don't tell Simon that -- he might take it the wrong way.· No, that's not what I meant. You take everything the wrong way.don't take this the wrong way (=say this when you want to give advice or ask something that you think might offend someone): · Don't take this the wrong way, but could I stay at your place tonight?
► get the wrong end of the stick British an informal expression meaning to make a mistake about one part of something that you are told, so that you understand the rest of it in completely the wrong way: · Maybe I got the wrong end of the stick. I thought she was leaving him, not the other way round.
► be at cross-purposes if two people are at cross-purposes , each of them thinks that they understand what the other is talking about, when in fact they are talking about two different things: · I think we're at cross purposes -- I'm talking about John, not Nigel.
► don't get me wrong spoken say this when you do not want someone to understand something wrongly or be upset by what you say: · I like Jenny, don't get me wrong, but I do think she acts a little childishly at times.· Don't get me wrong, I love my family, I just don't want to be with them all the time.
► lose the plot British spoken to suddenly be unable to understand what is happening in a situation, especially when people expect you to understand and deal with it: · In the past few days the President seems to have completely lost the plot.
at cross-purposes if two people are at cross-purposes, they do not understand each other because they are talking about different things but fail to realize this: 
I think we’re talking at cross-purposes.