How could you politely end a conversation with a person who is so annoying?

If someone is annoying and you want to end the conversation, I might explain that we all have opinions and not every ones opinion is the right answer. Sometimes we have to look at both sides to make an informative decision. My mom used to tell my sister and I to act like the other person and how would they feel about their side of the discussion. This can help us all think about both sides of that discussion.