Arrogance lead to destruction.
The Jedi Council faults into letting the Sith overthrow them are 2:
1. Being too much involved into politic:
Acting in this way they become more kind of elitè soldiers than Jedi Knights, they were forced to discuss with the Senate and politicians, while an order like that of the Jedi should be a kind of superior power able to operate for peace and justice with being merely influenced from what the Senate sayed or decide.
2. Being so such arrogant:
Jedi Council wasn't sufficiently focused into using the Force to feel what was gonna happen or to detect incombent dangers.That, mixed with Sidious outstanding control on the Dark Side, let the Sith acting under the nose of the Jedi, they were sitting near their major enemy everyday without even suspecting of who he really was.
Plus their convinction of the Sith Order being extinguished, make them acting in that foolish way.Yoda himself always sayed that the Dark Side is hard to detect, but come on, all those powerful masters with Yoda himself didn't even try to organizate an assembly of the Council after they discover that Maul was a Sith to use their force powers to detect other Dark Side users.They feel they can handle the return of the Sith and the result was they get a collective asskicking.
Major arrogance will be showed from Windu, 5 Jedi to arrest a Sith, but if he knows that Palpatine maybe the Sith Master himself, he should took in the Chancellor lair 10/12 Jedi and wipe the floor with him.