When you start a statement with "no", "but", or "however", no matter how friendly your tone or how many cute phrases you throw in to acknowledge the other person's feelings, the message to the other person is YOU ARE WRONG.

It's not "I have a different opinion". It's not "Perhaps you are misinformed". It's not "I disagree with you". It's bluntly and unequivocally, "What you are saying is wrong, and let me correct you. I know better."

Nothing productive can happen after that. 

The usual response from the other person is to oppose your position and fight back. From there, the conversation dissolves into a pointless war. You are no longer communicating.