In critical thinking, the intentionality fallacy is when someone tries to insist that their statement must mean what they claim it means, despite their words indicating something different.
Here is an example:

Mac: "Hey Jack, I need you to pay back the $100 I lent you yesterday."
Jack: "But it's only been a day. The promissory note I signed just says 'to be paid in a timely manner.' You are the one who wrote that!"
Mac: "Yes, and by 'timely manner', I meant the next day. Which is now today. Pay up, please!"
Jack: "If you meant that, you should have written it that way."
Mac: "But since I am the one who wrote it, I know what I meant. So, I hereby declare that is what it means."
What Mac means by his words is up to him, but what his words themselves mean is not up to him. Language is a social phenomenon -- it is public property. So Mac doesn't get to dictate what a phrase means. The phrase "in a timely manner" is commonly understood to have a flexible meaning and does not automatically mean the very next day. Mac can ask to amend the note with a different statement, but he cannot insist that the note means something that it doesn't -- even if he himself is its author.
Note that this fallacy is distinct from the "intentional fallacy" in literary criticism, which questions whether interpreters of a text must try to reconstruct the author's original intent.