Definition
To falsely suggest that someone meant something different from what they actually said, often by misrepresenting or exaggerating their words.
Please don't put words in my mouth; I never said you need to resign, I only suggested you might consider other options.
The media often puts words in politicians' mouths to create sensational headlines.
I only said there are potential risks with the plan, don't put words in my mouth and say I'm completely against it.