Argument 1: That it's an illogical course of action to take because we don't know that synthetics rising up against their creators is an inevitability (and that the Geth prove it).
So we should've killed all germans in WWII because they can't be trusted?
Also Shepard reply that without hope - or "naive idealism" - we are pratically machines and this sustains the organic humans in difficult times.
My main problem is not the lack or prevalence of logic, is that Shepard is totally submissive to the Catalyst.
Also the Catalyst don't argue about this particular statement, giving the impression he doesn't or are unwilling to take it into account.
A sentient machine appears to be able to take thousands of scenarios in their conclusions, like EDI does and sucessfully prove it can be done.
And the Geth are the proof, because they contradict the Singularity concept.
In the article you provided is stated: "The AI does not hate you, nor does it love you, but you are made out of atoms which it can use for something else." (Eliezer Yudkowsky).
But guess what, Legion and even the Geth VI says they admire the concept of hope and cooperation of the organics and are willing to emulate (or upgrade them) this concepts.
Also remember the Technological Singularity is a "concept", not a theory.
Argument 2: That the Starchild's argument is cyclical (creating synthetics to kill organics in order to prevent synthetics killing organics).
Again using the same example, we had a certain person 70 years ago that stated that a particular race "are undoubtely a race, but is not human".
Then he try to exterminate them.
And this make sense?
The peace with the Geth will last? I don't know. The Geth will turn against organics after Shepard giving them the final stage of their evolution? I don't know.
The synthetic Geth will turn against the organics humans, asari, turians and salarians for certainty in the future? Excuse me, there's no proof whatsoever that support this will happen regardless.
Remember the Geth Prime and Legion said Shepard improved the opinions of the geth about organics and they will hold to this.
The Geth evolved into something different than the Reapers and Legion is also different from the other Geth, given the perspective he gainned when joining Shepar in the Normandy for the first time.
Javik and the Catalyst stands that machines don't change, but the course of the events proven them wrong.
Argument 3: That the Starchild could simply destroy the synthetics instead of destroying the life that creates them
My main problem is not that the Starchild could simply destroy the Reapers, my main problem with this particular line of thinking is what the hell he was doing when Sovereign invaded the Citadel?
Playing chess? Babysitting his little baby Reapers? Not even a "hello son, I created you, do you need help against those pesky ships"?
This logic itself pretty much throws out the window the entire story of ME1.
If the Catalyst is the Citadel, why on Earth he needed Saren to activate the Citadel master control? How the Protheans were able to corrupt the signal to the keepers if he's the Citadel?