High drama approach to quality feedback?

I've got a direct who is not hitting the competencies I expect at his role level. He's been in role for 14 months now, moving from a manager to a director. He made that move relatively quickly, perhaps a year if that into his first management role. I've been in the organisation for about 9 months now. He's struggling to make the adjustment to director. I've provided regular positive feedback, moving to corrective as well in the last three months.

I've just had his first quarterly review since we moved into corrective feedback. In this most recent quarterly review I repeated, in writing, some feedback I'd given him verbally through the feedback model. The review is very forward facing (where you didn't achieve your objectives, what's the manager's reflections of how they could do differently in the future and what are the lessons learnt - a coaching framework). I'm not interested in rehearsing the past and focus our monthly catch ups and quarterly reviews as a time we can really dig into professional development. I've had a lot of success working like this, and really enjoy coaching my team.

My challenge is our different level of assessment of his abilities which is making it difficult for me to coach. He was absolutely thrown by his review, where he got a 2/5. He had scored himself a 4. I rarely score a 4 and my team are well prepped that a 3 is very good, a 2 doesn't mean its time to panic but does mean its time to reflect on where you need to improve. A 4 regularly is when we're starting to talk about promotion or moving to a new role elsewhere. 

He has taken getting a 2 very hard, and sent a long email with suggestions of how to improve. Mainly on how I can! 

His main wants are framed as support he wants me to provide him, but to me, the kind of support he wants is reflective of managing people at a much lower level. For example, he wants to use me as a sounding board for his ideas so I am there to give him the OK on the work he's doing, and also he wants me to take on the bits of work he finds difficult so he can concentrate on where he feels most skilled. Some of his feedback has been that he does not make good use of my time, and that he delegates his work upwards to me and someone more senior than him rather than down to his team - so this feels like the same thing? At times, it feels like he's approaching me like his PA rather than the CEO of the organisation he works for. 

On reflection, its feedback pushback. What's thrown me is that it's destabilising my approach. I know in every professional balanced way I've ever worked that it doesn't pass the middleman test, that its wild he's expecting the CEO to take notes for him so he can concentrate on thinking, and that its a unreasonable expectation for his boss to staff him. But, in the moment, its making me second guess if I should be providing this level of support for him?? I suppose I'm after a sense check from other people who make use of MT. This isn't reasonable, right?! OR lay it on and tell me I should be doing more for him to get him up to speed. Thank you!!