Hey, argument after the fact is my line about Leviathan. 
That's why I had to get it in first 
I'm talking about it internally though. I gave a possible idea on why the leviathans might not be able to use their mind control abilities. As for teaching their thralls, it seems to be their argument that it's in organics nature and couldn't be simply taught away.
I guess it could fry their subjects' brains like indoctrination does, but I figured that was a side effect of artificially generating the effect. It doesn't seem to have the same level of finesse as the Leviathan's. If they've got to manipulate their thralls as much as control them, I don't see that they'd have the same belief that they're the galaxy's apex race. That does rather suggest complete control from the effect.
And looking at the Geth, all it's going to take is some simple precautions. If the Quarians had simply limited the size of the networks the Geth could achieve, and created specialised units dedicated to particular tasks, the Geth would likely have lacked the ability to evolve as they did.
As to why they would make their own AI, the Leviathan gives an answer to that. It's still a good question, but you can again chalk it up to their arrogance.
I could see arrogance working if it was just an AI designed to oversee various things, but they created it to tackle a specific problem that they'd become aware of. They were forewarned, and aware of the problem enough to take action to counter it. Considering that they'd seen it happen consistently and repeatedly, creating a synthetic construct to solve the problem of synthetic constructs rebelling isn't arrogance, it's stupidity. It's like seeing someone shoot themselves accidentally by fiddling with a loaded gun, then picking the gun up yourself and fiddling with it.
But then again, I suppose you have to expect this kind of thing in the Mass Effect universe, and ME3 in particular.
While it would make sense for the leviathans to care about their thralls fighting each other, the Catalyst clearly does not.
I was thinking more in indirect terms with the threat to other thrall species. All it takes is for one of them to make a construct a little smarter, and the AI could deem it a threat to the other races. It could just end up killing them just as surely as the constructs would have. (And I'm not just saying that because that's pretty much what it did.)
Only organic versus synthetic is special.
Okay, but that just underlines the stupidity of creating the intelligence in the first place. The AI is too specific, in that it deals solely with organics versus synthetics, but its mandate is so vague and open-ended that you'd have to be ignorant to the very nature of the problem it was built to solve in the first place.
Urgh, I think I'm going to have to abandon this whole train of thought, before my head explodes. They could have done something really clever with this, focusing on some property or other that synthetics lack compared to organics, even if it's only in the ME universe, but instead they went with this mess.