I've gotten used to this move, as it's part of my daily routine. It's probably the hardest non-aerial move there is though
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It's all about positioning. if it's too far into the web of your thumb, it's going to start turning. If it's too far to the side, you're going to drop it.
I suppose you could gauge it like this: keep your 4 fingers together, and keep your thumb out to the side so that your thumb feels comfortable. the direction you want the balisong pointing (or to go) is parallel to your fingers.
When I do them I make a small counter-clockwise circle with my hand to guide the balisong. I think it gives it more inertia.
Now you should be holding only the bite handle with the inside of your thumb when you drop the safe handle. You just gotta let the safe handle drop, and when it's pointing to the ground, start the counter-clockwise motion with your hand and let go of the bite handle. Catching it without cutting yourself is a little difficult- I usually don't cut myself when I mess up, but I just catch it closed or something. So my advice to you is to practice just the rotation over your thumb and then drop it, THEN when you're comfortable with it, make the catch.
Or make the catch all along; doesn't matter