Sounds simple to answer, but it is not. As a matter of fact, brilliant minds failed to give a reasonable answer. The "vibration effect" that you may already have come up with is not the cause of the second fracture. Because if you make the same experiment inside a water tank to absorb the vibrations, the spaghetti will still break in at least 2 points... So what is it?
Well, I will not spoil the following video - It is very well narrated and drives you through the research step by step.
Photo: Frames from high speed video of bending pasta strands, courtesy Daniel Ridley-Ellis.