Words don't mean the same thing to different people
What is assumption of common meaning and why is it a problem?
Some people believe that words mean the same thing for different people. After all, don't we have dictionaries so that people can have the same understanding of a word? This is a major problem in communication -- not realizing that language, any specific word, can have a different meaning for one person compared to another.
Here's an example. You are talking to someone who is considering buying a pet. For you the word "dog" has very positive meaning, since you had dogs all through childhood. So, you suggest to the person that he might buy a dog for companionship.
But does the word "dog" mean the same thing for the other person? That person may have been bitten by a large dog, when he was a child, and has developed a terror reaction to most dogs. For him, the meaning of the word "dog" (it's connotative meaning) is completely different from yours. If you are oblivious to the idea that words carry different emotional meanings, you and the other person can never learn to understand each other.
Even with seemingly straightforward word definitions, things aren't simple and we can't assume that when one person uses the word "liberal", for example, that they mean the same things as you might mean. For him, a liberal might mean a cowardly, crime coddling and socialistic thinking person, while for you, it might mean someone who believes that we should help those less fortunate.
The more heated and emotionallly loaded the words we are using, the more important it is to first try to understand what the other person means from the words he or she uses. Many arguments and conflicts can be prevented by trying to understand first, then "argue".