Bottom line for this? #1.
The point is that organic evolution began all this. Organics evolve, gain capacity to create machines, begin (intentionally or unintentionally) 'breathing life' into the machines, and then something has to be done about the machines, and so forth.
So I guess even before the Leviathans, it would be the first organic species in the galaxy that created a robot?
But anyway, yes, #1. The Catalyst, whatever it is, was made to ensure that the Leviathans continue to 'care for' the other organics that 'pay tribute' to them. Synthetic/artificial evolution messes up the 'natural' order of things, where the simply most powerful species lord over the rest of the species.
To guess, I'd say that Leviathans won a billions/trillions of years long fight to be the strongest organic species. Anything beyond them would be extragalactic. So the only thing in their way was the fact that organics beyond their reach kept making synthetics. So yeah, they were arrogant.
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Regarding #2, I don't think the Leviathans believed that the created will rebel against their creator. They, like heck, many people here, don't believe it as an inevitability when you treat any intelligences badly. They considered synthetics to be tools that go faulty. So they make their own tool that protects organic life (otherwise a synthetic would overcome the Leviathans and all other organics and possibly make sure no organic life even gets to exist), and tries to establish a connection between organic and synthetic so that there wouldn't be a need to protect organic life.
As Leviathan states, it still serves its purpose. Organic life itself is allowed to continue, and have cycles of 10,000s of years of civilization. Synthetic life outside the Reapers is held back, unable to grow powerful enough to eradicate organic life. Previous organic life is preserved in a still unknown-ish Reaper form so that their knowledge and possibly more, are utilized in the collective intelligence in order to at some point find an actual solution to this paradoxical problem.
And before you think of the Geth letting some Quarians go, keep in mind that this is a synthetic 'species' that outright idolized their creators and highly respected them, even as they committed unemotional genocide in response to them. They are actually that specific synthetic species (like humanity and co are the specific organic species) that exist in a cycle that JUST MIGHT give hope to solving the problem. Organics might be open to positive relations with synthetic Geth or more. Geth might be open to understanding organics enough to not decide to wipe them out (but clearly the case with GethVI doesn't have as positive implications).
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Regarding #3, no, I don't think Leviathan(s) have a death wish.
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So to bring it back down to the bottom bottom line, the Leviathans made this mess. They are demons (in the deep) that, through their actions and attitudes, created machine god-devil-angels that are only barely restrained from obliterating life in the galaxy. The Reapers are not good. They do believe themselves to be superior minded. But we just get to see over time that most major Reapers are actually of a synthetic-organic mix (ME2, and still more synthetic than organic), and then that a synthetic intelligence acts as the collective of their intelligence and acts on what they learn (which isn't much, as this is a cycle of DEATH and REAPING), and we can optionally learn that it was organics that set that synthetic intelligence up in the first place, because... organics and synthetics were not getting along.
If there's one thing I don't want Mass Effect to drop, it is the concept of cycles. We may have broken the Reaper cycle in some way, but there's so many cycles of stuff in other cases (between even just organics), that there's gotta be some other system happening on top of the Reaper cycle.