It's not based on the Yo Dawg internet meme. It's literally what the Catalyst is telling you. And I'd wager that that I've spent more time playing the game than you. Because I don't like going outside.
The catalyst's axioms are debatable.
But it's logic is not flawed, unless we over-simplified it.
his race of synthetics are destroying organics to prevent organics from creating a race of synthetics that will destroy them is not a correct sentence.
a. "his race of synthetics"
reapers are not synthetics. They are hybrids, created by harvesting organic races. Their mind, consciousness, "soul", is largely organic. They are not "ordinary" synthetcis: they are something more and something different, a primitive example of synthesis. To them, the "conflict rule" (synthtetics will always try to destroy organics) doesn't not apply.
b. "are destroying organics"
they are not destroying them, they are harvesting them, preserving them in reapers form. But let's say that this is madness and harvest = extinction. They are destroying only 10-15 species every 50.000 years. They are destroying the 0,0000000000000001% of organic species in the galaxy.
c. to prevent organics from creating a race of synthetics that will destroy them ALL.
The last word is the key. The catalyst believe that, in the long term, sooner or later, synthetcis will became so advanced, so powerful, that all organic life (and not only the 0,000000000001% harvested by the reapers) will be at serious (inevitable) risk of extinction.
His (debatable: shepard can choose not to believe them) axioms are:
1) Tech singularity is inevitable, if advanced organics are allowed to create more and more advanced synthetics
2) Tech singularity will cause the extinction of all organic life
So the catalyst is using a unique, hydrid race to "destroy" an infinitesimal percentage of organic species, in order to prevent them from creating a race of synthetics that will reach tech singularity, and cause a mass extinction.
EDI and the geth prove nothing.
Simply, a sexbot and a single synthetic race are collaborating with organics from a couple of years and a couple of months. So what? The catalyst's reasoning perspective is billion of years, billion of species... a momentary cooperation disprove tech singularity? I don't think so.