I believe, this is mostly due to our not being familiar with the basics of logic.
Most of us learn our languages informally and used to imprecise meanings and learnt to live with them. To avoid this, in the future, try leaving on the family coffee table a few pages from a concise introductory logic book. Before long you will be surprised to see, family conversations that are more fruitful and harmonious.
you make one assumption that has been demonstrated to be wrong. What you say would be true, IF Humans were rational. They aren't, especially when it comes to issues with a strong emotional element. Humans like to *rationalize*, i.e. they like to use logic to justify their irrational actions.
A demonstration of this is one you mention - Most of our languages, English especially, are in themselves inherently imprecise or ambiguous.
Mr. Shmuel-Aharon Kam - I agree with you that as human beings we rationalize (using a perverted form of logic) our actions/emotions. The solution is to learn the correct form of logic, which will prevent us from committing fallacies in the first place. All languages have words that are imprecise and ambiguous. By learning those limitations, I am able to communicate better, I think.