Common idioms:
* Talking at cross purposes: This is the most direct and common idiom for this concept.
* Talking past each other: This emphasizes that the people involved are not really communicating with each other.
* Be on different wavelengths: This highlights a lack of understanding or shared perspective.
* Speaking different languages: This suggests a fundamental disconnect in how people understand and interpret information.
Less common idioms:
* At odds: This suggests a disagreement or conflict, which can be caused by talking at cross purposes.
* Talking in circles: This implies a lack of progress in the conversation.
* Missing the point: This focuses on one person not understanding the other's message.
* On opposite sides of the fence: This emphasizes a stark difference in opinion.
The best idiom to use will depend on the specific context and the nuance you want to convey.