To be fair, immortal machines can't help but have a different frame of judgement to super mortal organics. What's killing a few to save the concept of life? Where was the fallout 1 esq* side with the reapers choice?
Their killing isn't logical though. It's not a "kill one man to save a million" scenario (or in MEs case, kill billions to save trillions?). It's nonsensical bullshit. Destroy entire galactic civilizations because they MIGHT create rebellious AI that MIGHT wipe out all organic life in the galaxy for some unknown reason.
Since we know the reapers leave some behind to observe during the 50k year period, would it not be more logical for them to simply wait for the rebellious AI to be created and then destroy the AI?
Would it not make even more sense to not jumpstart civilizations by leaving behind mass relays and artifacts from previous civilizations (i.e. Prothean ruins on Mars) that facilitate progress?
Would it not make even MORE sense for the reapers to just be an ever present force in the galaxy ruling over organic life and demanding they never create AI?
The whole reaper cycle doesn't even make sense. Apparently creating a reaper is a super rare thing (only one species in the current cycle was even a candidate for it apparently) and they lose several reapers in the battles before the crucible is used (and in that battle). How do they keep up their numbers? During the Prothean cycle they fought for centuries, the probably lost hundreds of reapers. If they are losing more reapers per cycle than they create... how are they maintaining their numbers? We know they didn't make Prothean reapers because they turned them all into collectors.
failure to communicate. Apparently though, the Catalyst wasn't up to the job, as it states that 'our efforts always ended in conflict, so a new solution was required': the Reapers.
As for the two 'mights': the galactic civilizations already have created rebellious AI; most notably the humans and quarians. The Catalyst, reasoning that synthetic life will always come in conflict with organic life, considers it go-time because it is 100% convinced that organic life will lose that conflict. The reason for the inevitable conflict is unknown, or perhaps there are dozens of different reasons. Either way, the reasons are not important to the Catalyst because it has already finished it's research, so to speak. Or, based on its statement that the Crucible created 'new options', the Catalyst might not have been capable of coming to a different conclusion in its original hardware setup. That's all speculation though, and will probably never really be cleared up.
The Reapers aren't perfect, either. They missed Ilos, they missed Javik, they probably missed dozens of worlds. Wasn't Feros one big Prothean ruin? The Catalyst also admits that it knew of the Crucible in previous cycles but that it thought the design had vanished.
Who knows, I think it could've been fun if they had made more of an issue of the Catalyst being wrong - because I think that is actually quite an interesting topic. What if the advanced AI is wrong? Why is a supercomputer wrong - how could it be? How does one come to a correct conclusion, etc. But that's a different theme than what they were going with and would have required a lot more build-up in the earlier games to come off decently - if it's even a good idea, which I - being far from impartial - can't comment on. Either way...