While the Jedi were arrogant, and that was their secondary flaw, their fall was mostly due to darkside influence. Palpatine's and Plagiues' experiments had thrown the whole galaxy out of balance, and so by the time of the clone wars, the entirety of known space was under a cloud of the darkside, I believe.
Additionally, it wasn't arrogance that caused the Jedi's fall, it was how over time, the original teachings of the Jedi order had become distorted (I would recommend checking out the original Jedi code in comparison to the code from the clone wars). The clone wars code says "there is no emotion, only peace", whereas the original code said "there is emotion, yet peace". This is where the Jedi went wrong; the old Jedi order would never have told Anakin to not mourn or miss his Mother after her death, and instead would have said "there is death, yet the Force". The Jedi fell because they had corrupted the light side into something different, not because balance requires a roughly even number of force users trained to roughly the same degree on both sides. Balance is not about head count, as Chronicler said, it is about the eradication of the Sith entirely, if not Darksiders on the whole. Sith bend and subvert the force to their will, and thus are in constant conflict with it. The Jedi, on the other hand, allow the force to flow through them, and thus they act as a vessel for it. Darth Vader completed the chosen one prophecy in episode 6 when he killed the last Sith, not in episode 3 when he sacked the Jedi temple.
Edit due to spelling mistake*