It could come off the wrong way to the interviewer. For example, if you said "I received offers from competing firms and leveraged that to get an interview at McKinsey", that will put doubt into the interviewer's mind about your committment to McKinsey.
Additionally, it may seem as though one of your biggest achievements in life is getting an interview with McKinsey. In the grand scheme of things, this is not a really big deal. The interviewer could interpret this as you lacking the accomplishments of him and his peers.
It could come off the wrong way to the interviewer. For example, if you said "I received offers from competing firms and leveraged that to get an interview at McKinsey", that will put doubt into the interviewer's mind about your committment to McKinsey.
Additionally, it may seem as though one of your biggest achievements in life is getting an interview with McKinsey. In the grand scheme of things, this is not a really big deal. The interviewer could interpret this as you lacking the accomplishments of him and his peers.