On the job, many clients may resent your presence. They may have worked 30 years in the industry, and wonder how you can possibly be helpful considering you've worked 3 days in the industry.
Other times the project you represent threatens their job security, so the client is not very enthusiastic about helping you.
Different offices test these skills in different ways. Some ask you what you would do in a certain situation -- a leadership case interview. Others want you to do a role playing exercise with them.
Here are links to the McKinsey Team Leader game that illustrates what McKinsey is looking for in both the leadership case and role play interview.
The following links all point to the same game, but are hosted by different country-specific websites for McKinsey