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The problem with this is that Monarch sees Godzilla as a force of nature that maintains a balance, so I don't see why they want Kong to believe that the King of Monsters is bringing chaos and destruction

We really don't know what Monarch's official position is on Godzilla. They seem to be just a small "X-Files" organization. Not some grand scale conglomerate with military power like S.H.I.E.L.D. It was really just Serizawa's opinion that Godzilla was a form of natural balance.

As for the theory, I'm not sure Kong will be anthropomorphized to such an extreme. I still believe he and Godzilla will team up against another threat, but I don't think their clash will be influenced largely by man.

My theory on Kong growing big enough in the first place to take on Godzilla is that he'll discover a rich radiation deposit that'll allow him to grow exponentially larger.

Godzilla finds this, and now sees Kong as a threat to the balance where he wasn't before. Godzilla goes to Skull Island to nip this in the bud, but ends up accidentally killing some of the Iwi in the process. This, combined with the natural territorial nature of animals, would lead Kong into conflict with Godzilla.

Just my thoughts, though.