She was the only one who possibly had both the motive and the authority to do as Zircon had deduced. (Blue questioned that Rose shattered Pink - who would bring that up if they were the quilty party and their enemy would have taken the fall?) (Yellow's fury at being accused and strict-motherly interactions with Pink convinced me that she couldn't be the one.) (White's motive was likely to remove the "defective" Diamond from the ranks, perceiving her as a potential (inadvertant) threat to the Homeworld.)
She seems to have higher authority than the other Diamonds (being the head and torso of the Gematron, and the top Diamond in both symbols), and thus would be the only one able to order the Gems to keep a secret from the other Diamonds.
She doesn't appear. This means that we don't know her personality whatsoever. She could be anything from unhinged and power-hungry to emotionally dead, all of which would give her more motivation than the other Diamonds.
I believe that White's largest concern by far is the objective advancement of Homeworld, at the cost of emotional ties and the subjective - which ties back to her motivation.
On a related note, has anyone considered that White might be the same size as (or even smaller than) Pink?