This is a classic example of a self-referential paradox known as the liar paradox. Here's why it cancels itself out:
* If the statement is true: If "This statement is false" is true, then it must be false, which is a contradiction.
* If the statement is false: If "This statement is false" is false, then it must be true, which is also a contradiction.
This paradox highlights the limitations of language and self-reference.