It is a myth that knives are prohibited for self-defense in any state. It's not that there is any law about it, it's that cops questioning you about it will have their judgement of the matter affected. There's generally two reasons for this, with some overlap:
1. Psychological research on cops shows a strong tendency toward the belief that
only police officers should have the ability to dispense physical force and stop criminals. A citizen who is readily capable of defending themselves therefore may be seen as doing the officer's job for them, effectively robbing them of their self-identity and purpose. Therefore, when an officer is told a person has a object for self-defense, there is an immediately feeling of resentment towards that person and if the laws of the area are not very clear on the matter, they will try to spin them toward the carry being illegal, sometimes even confiscating it when it's otherwise a legal item while not making an arrest. This should never be mistaken as actual law and the officer is technically committing theft when this happens. This is an unconscious matter and the cop is not aware why he or she is doing it; they often try to rationalize it with flawed concepts like "it will just be used against you."
2. The other reason is in areas with "intent" built into the law as a function of legal carry. Carry for self-defense still counts as
carrying with intent to use as a weapon, even if that usage itself is not per se illegal. This is because an act of self-defense is actually an act of assault or murder until proven otherwise; it is an affirmative defense for the courts, not a legal immunity.
I will say that the balisong is probably the last weapon I would ever use for self-defense. I don't care how fast and dexterous you are with on, I can open a fixed blade and stab with it faster. I can probably open most folders faster too if it's one I'm accustomed to. And that's not even when you start breaking down the practical issues of using blades in self-defense overall.