Primacy Of Consciousness
The interdependence theory accepts that consciousness requires (or "implies") existence (C -> E), and then proposes that at the same time, existence requires consciousness (C <- E); or taken together, (C <-> E).
Where this is wrong is in dropping the context of what consciousness actually is and does. Consciousness is the faculty which perceives that which exists; it identifies existents. That is its definition: that is what it does (what we observe it doing). More specifically, it takes in sensory data, automatically transforms it into percepts, identifies the percepts, and then internally manipulates the data.
Consciousness exists as a specific type of existent with a specific identity. To claim that it does any thing other than what we see it doing is completely arbitrary and without merit. Making the claim "existence requires consciousness" is as valid as the claim "existence requires this table" or "existence requires a large maple tree." - arbitrary, without any basis in reality, without any evidence, and also quite absurd.