So what I really meant was…
“I see it differently. What I understood was…”
Change the “you” message to an “I” message. If you say what you currently see, think, or feel using an “I” message with an adult tone of voice, as opposed to a child or parental tone of voice, you’ll have a much better time getting your message across effectively.
Limit your “I” statements to the facts and your feelings, while trying to avoid judgments. Saying “I think you’re an idiot,” for example, is a “you” statement in disguise, and therefore a negative judgment, inviting animosity and antagonism, instead of clarification and conciliation.
On the other hand, it’s hard to become defensive or disagree when people explain their viewpoints from a personal standpoint, “I understood…,” “I believe…,” or “I want….” This kind of communication encourages dialogue instead of diatribe.