Question

give an example of a mismatch between the message of a person wants to communicate and the medium he or she chooses to communicate it with?

Answer 1

If you've read Outliers, there are great examples in that book.

One such is example is the hierarchy in Asian nations and how they affect plane travel. Subordinates will often not confront their captain of a plane if danger arises. Often they chose silence as their medium.

A more simplistic version:
Someone falls to the ground in a public area. They are having a seizure. Someone notices and calls out for others to phone the police while they write a note to the cops about what happened.

Answer 2

An example can be, when someone tells his colleague that he is feeling well but the facial expression, anxiety from his face and body language doesn’t support his statements, the person receiving this information will not believe his words but rather the non-verbal communication being relayed.

In this situation the message is "i feel nice" but the medium he is using, his body, is showing signs that doesn't match with the message.