I heard once that a woman need only look at the way her boyfriend treats his mother to see how he may treat her someday. The same thing applies to candidates in an interview.
When I am interviewing a candidate, I want to imagine them doing the job for which I am interviewing. I want to imagine how they would behave not just in the specific job, but as a member of our team. I want to know that they'll be part of the team even when things aren't going perfectly, and will accept responsibility for their part. And I want someone that will be proud to be part of the team.
One easy way to give the interviewer the impression that you are not part of the team is to use "they" in place of "we".
For example: an interviewer may ask you about the type of business your current employer is in. There is a big difference between, "They are a widget manufacturer that specializes in polymer widgets" and "We are a widget manufacturer, specializing is polymer widgets".
Pay attention to when you're using "their", "them", or "they". Oftentimes, using "our", "us", or "we" can come across more inclusive.