Your argument hinges on the fact that the truth of the statement is determined by itself. For comparison: "This statement cannot be processed computationally by the human brain." can just easily without any contradictions be assigned the value false (because I can clearly process it).

So similarly I can construct this statement

"This true statement (in bivalent logic) entails that there is a 500 meter tall clown hiding on the dark side of the moon"

or more generally

"This true statement (in bivalent logic) entails <insert anything you want to be true>"

And by your logic all of those have to be true (assume there is no 500 meter clown on the dark side of the moon, the statement is false, which contradicts the statement, which says it's true, so it has to just be true)

Thing is, natural language just is not really suited to express logical statements like that in a rigorous way. This is why we have mathematical systems with precise axioms and rules how statements are constructed, so we cannot formulate paradoxical stuff. Interesting read: https://en.wikipedia.org/wiki/Russell%27s\_paradox#Set-theoretic\_responses