This is, of course, completely understandable - they have, after all, only just been selected for the role they are new to and it is a difficult thing to admit one's weaknesses. It is, however, fantastically important to understand your own skills sets - and particularly to know which skills you are missing. Those areas in which you need some help.
There is nothing wrong in asking for help - I do it all the time. Anyone who knows me will be aware of my weaknesses in marketing myself. I understand some of what is necessary but I'm just not very good at it. I'm very lucky that I don't need to market my business too much - but I know that I need help every so often and so I have a list of people who I ask for their professional help and advice.
Having asked for help, I am now very careful to listen to my expert. I too have fallen into the trap of saying "Yes I know" as someone who knows a great deal more than me in a specific area tells me something. I too have found it difficult to hear some criticism and to amend my own behaviour.
Having acknowledged a weakness it is vital to (a) find and expert and the (b) listen to them. That sounds very obvious - but I do spend a great deal of my professional life stating the obvious - that often seems to be my role.
I'm good at what I do - and so are other people, I'm no longer afraid to admit it. My name is Peter and sometimes I need some help!