A Virtual Chief Performance Officer frequently runs into a roadblock that I call "The Lizard".
I'm guessing you've run into "The Lizard" in your work.
You wonder how the heck this person ever got into a position of authority? He appears to have minimal mental capacity to balance competing ideas in his head. Maybe your analysis says that you have to have a robust pipeline of new customers to be successful, and he is a loyalty advocate. He's gonna "go binary" on you and argue that loyalty is the path to success, and he'll reject every acquisition-based argument you provide, regardless of facts. I mean, it's possible for numerous things to be truthful at the same time. You can improve customer acquisition efforts AND you can improve loyalty efforts.
The Lizard generally doesn't hold competing thoughts in his head at the same time.
The VCPO must become very, very clever dealing with somebody employing Lizard Logic (i.e. binary thinking).
The VCPO writes objectives for The Lizard that align with the binary thinking that The Lizard can handle.
The VCPO then writes objectives for everybody else, and separates accountability for succeeding at those objectives from The Lizard.
I realize this means that The Lizard might benefit from the work of other people, but that's life. Why do you want to have non-stop arguments with an individual who isn't capable of thinking beyond binary choices?
If your CEO is "The Lizard", well, you've got problems.
But if your Chief Marketing Officer is "The Lizard", well, that one is not difficult to work around. Set specific goals for the CMO that "The Lizard" agrees with philosophically, then work with everybody else to implement other ideas.
Get the data, analyze the data, then work around personalities that hold back company performance.