It's one of the more commonly misunderstood aspects of the conflict, but the clues are there if one pays attention: in short, both sides were convinced that the other side was the aggressor, and both sides thought they were pre-emptively defending themselves. This is all of course entirely by Sidious' design. And despite assumptions to the contrary, the Jedi *really* didn't want to be involved in any of this. They practically had to be dragged kicking and screaming into the role as Generals.
First, it's probably best to unpack some of the events of AotC. To start with, the opening crawl lays out the basic set-up: -
There is unrest in the Galactic
Senate. Several thousand solar
systems have declared their
intentions to leave the Republic.
This Separatist movement,
under the leadership of the
mysterious Count Dooku, has
made it difficult for the limited
number of Jedi Knights to
maintain peace and order in
the galaxy.
Senator Amidala, the former
Queen of Naboo, is returning
to the Galactic Senate to vote
on the critical issue of creating
an ARMY OF THE REPUBLIC
to assist the overwhelmed Jedi....
While it's light on specifics, from this we can infer that increased tensions, unrest and civil strife has been building for a while. The Jedi are becoming stretched thin trying to keep a lid on things, hence the call in the senate to vote on the military creation act to increase security, and restore order (in theory.)
Padme says she's been working for a full year to defeat the military creation act, asserting that if the army is approved, the Separatists would interpret it as aggression and it would push the Republic into a civil war. Tensions have to have been already very high before even that, so this isn't just some recent flair-up of unrest but a sea-change in galactic politics that's probably been gaining inertia for most of the last decade.
Remember that this is no small movement; it's *thousands* of systems that have already declared an intention to leave, with (according to Dooku) tens of thousands more likely to follow if they do. That's a non-trivial percentage of the entire Republic proposing to split the galaxy asunder, potentially causing utter bedlam to galactic trade. Whole planetary economies could be wiped out, supply chains would evaporate overnight, billions would starve, and there'd be a refugee crisis on a scale unseen since the Sith conquests. Galactic civilization itself could collapse. So pretty high stakes, and ample motivation for the Republic to make sure they don't just leave and take half the galactic economy with them in the process, no?
By this point the perception of the Separatists is that the Jedi had become little more than enforcers for a corrupt Senate that no longer represented the best interests of the people. Any time they protest unfair treatment by the senate, or try and stand up for themselves, the Jedi are sent in to "keep the peace".
They felt they needed an army to protect themselves from the Jedi and force the Republic to accede to their demands.
So when the Senate found out about a massive delivery of military equipment from the Techno-Union on Geonosis, and a treaty with the Banking Clan, Commerce Guilds and Trade Federation, they took that as a clear escalation and intent to attack the defenceless Republic worlds (note: they didn't know about the secret clone army yet.) Even then, (thanks to the opposition led by Padme) most of the Senate would refuse to sign the act unless the Separatists attacked first. This is why Palpatine goaded Jar Jar into proposing to grant the chancellor emergency powers to end the debate and create the military before it was too late.
For their part, the Jedi had basically painted themselves into a corner. They were committed and duty bound to serve the senate, but they didn't want to become soldiers. Windu's mission to Geonosis was ostensibly only to "deal with Count Dooku". He was once one of theirs; and they just got very stark evidence that he's preparing for an all out war. Moreover they had evidence he had a direct hand in the assassination attempt on Padme, and had some unknown connection to this clone army that just seemed to appear out of nowhere.
That last part is important because the Jedi knew they'd been blinded by the dark side, but daren't admit that to the senate lest it make matters worse. A drop in confidence in the protection of the Jedi would only push the Republic closer to civil war. They needed to understand what was going on, so Yoda used the new army to try and capture Dooku and end the conflict before it really starts . . . and it failed.
At this point it might be worth mentioning some elements of the script that didn't make it into the final movie, but still indicate what's going on with the Jedi. Specifically there's a few exchanges (mostly between Yoda & Windu) that expand upon why the Jedi have become blinded. They should have foreseen the bombing attempt, and they know it. There's a great disturbance in the force and as was predicted by the prophecy, the power of the dark side is growing to the point where only through the dark side can future events be glimpsed. There were even some scenes of Yoda meditating and using the dark side to try and see through the fog. A very dangerous endeavour, obviously, but it speaks to the level of desperation of the council, mostly because it's been a decade since they learned that the Sith are alive and well and out there, and have so far not shown themselves again. They know the Sith are working against them, but they don't know how or from where the threat is coming.
Another neat little detail from the script is that although even after four trials and endless hearing the Supreme Court couldn't oust Nute Gunray as Viceroy of the Trade Federation, they did however order it to reduce the size of it's droid armies. Though rumours abound that they didn't actually comply with the order, and the Jedi were prevented from investigating as it would have been "too dangerous for the economy". Mention is also made of the other "armies of commerce", and the ongoing corruption in the courts and the senate that's allowed them to go unrestrained. That last part is important as it indicates how the Separatists were able to get their hands on such vast numbers of battle droids and ships; they were sold/leased to them from the Federation, the Techno Union, and the other Commerce Guilds already substantial forces, likely thanks to a substantial loan from the Banking Clan.
So, Yoda's gambit failed and Dooku escaped, likely using the unprecedented Jedi led military assault on Geonosis as proof that the Republic is moving against them, rallying even more systems to the Separatist cause.
At this point the Clone Wars begin, and it's mostly a four lobed conflict. The Separatist parliament is convinced that they're engaging in a holding action, acting defensively against Republic invasion and occupation of Alliance worlds (and since they're mostly droids, what's actually going on is easily hidden from them.) The Republic senate and the Jedi think that they are similarly acting defensively. Coming to the aid of systems that refused Dooku's "offer" to join the Confederation and instead suffered punitive actions ranging from neutralising them as a strategic asset the Republic can use, stripping them for resources (those Banking Clan interest payments have to come from somewhere!), or just outright genocide, which they then blame on the Jedi and use to scare other wavering worlds to join them.
For the Jedi, the priority is ending the war as quickly and expediently as possible, because they know full well they've been ensnared in a Sith plot, and the only way out of it is straight through . . . which is of course where the compromises start, and their fall begins in earnest.
