I am not sure I understand the feedback of the EM.
While there is some degree of dialogue in the McK interview, it should still be 80-90% of the time you talking. This is the main difference compared to candidate-led interviews. Your mindset should be that you are in the driver's seat and you are talking to the CEO of the company that hired you.
Therefore, discuss with the interviewer to
- play back their questions
- ask clarification questions to make sure you understand the situation and goal properly
- take time before each question to structure your thinking
- guide them through your thinking
- synthesize and elaborate on your hypotheses
These are the moments where the interviewer will reply. For the rest of the case, you are leading through each question until the interviewer proposes the next question.
From my experience, the more the interviewer has to talk, the worse off the performance is. For instance, this is demonstrated by the typical ''what else?'' questions during a structuring or brainstorming exercise where the interviewer is trying to elicit more information from the candidate in order to achieve a structure that would pass the bar of being
The structure of really strong candidates would be self-standing and does not require the interviewer to ask for more ideas.
Hope this perspective helps!