"How would adhering to this work against a specific gender? How could being an attentive, respective leader, who is vocally self-critical and candid be a bad thing?? Even if this could logically happen based on gender, of all things (and I can't for the life of me rationalize how) HR is in the room for promotion and review discussions to ensure that what Jodi and David refer to doesn't happen."

Clearly you have no empathy for gender issues. Discrimination is usually NOT logical, and as a man working in a leadership role, being a bit more humble about other gender's experiences and feelings would make you more credible. At all credible.