The script says that they’re arrogant, they’re naive and skeptical in regards to the Sith being back (understandable), and you have the Jedi librarian being a little bit arrogant, but everything else is better explained by simple lack of intelligence and poor detective work.
Being skeptical, to me, would be closer to, “I’m not sure.” I’m not saying they’re bullheaded or whatever, but arrogance, for me, doesn’t have to mean they’re utterly pompous about things.
Mace was not killing an unarmed man. It’s impossible to disarm him as he can (and does) shoot fatal lightning bolts from his hands, not to mention his extremely powerful telekinesis. Mace was 100% right, he was too dangerous to be left alive and had a stranglehold over every branch of the government. This was their last chance and Anakin bungled it. It’s a cool moment of ambiguity and internal struggle where Anakin starts out with “it’s not the Jedi way” and ends up with the more honest “I need him!”
Palpatine’s capacity for evil or actions I don’t see as a justification for preemptive action.
I know that’s a callback to Palpatine saying the same thing about Dooku to Anakin, but in this case it was right even if the script is countersignaling it.
Who says it was right? Who decides that?