To 'believe' is to assert the truth of something. Or perhaps better put, a 'belief' projects a subjective understanding onto the world as an ontological fact. Thus:
- "I believe in God" asserts that God is an ontological feature of the world.
- "I believe in evolution" asserts that the principles of the theory of evolution work as expressed in biological development.
- "I believe the Earth is flat" asserts that the Earth is factually flat.
Saying "I believe falsely" in the present indicative would be tantamount to saying "What I assert as subjectively true is subjectively false", which is mere nonsense. You could say "I used to believe X" or "I will believe X" or even "I want to believe X", and it makes grammatical sense for you to know that X is false. But it makes no sense to simultaneously know that X is false and assert belief in it.
This goes back to Wittgenstein's intuition that truth is always (at some level) a matter of convention. If we think about his discussion of a meter (Philosophical Investigations #50), we can know that something is a meter long by measuring it with a meter stick, and we can know that a meter stick is a meter long by measuring it against the standard measure for a meter (at his time a standardized bar in Paris; now the distance travelled by light in a fraction of a second). But we only know that the standard measure is one meter long because we assert it to be so. We all agree to believe that this distance is exactly one meter. That belief establishes the length of a meter as an ontological fact.