Perhaps the number one consulting skill, then, is critical thinking. Your customer will expect you to address complex issues affecting your business. They may have started the preliminary work and have a direction in mind. Or, they can trust you to start the conversation.
No matter how many frameworks, reference sheets, or strategy models you have up your sleeve, good consulting always comes down to analytical skills. What matters is whether you can effectively deconstruct and classify information, identify new correlations, and draw conclusions from all of this. Strategic thinking is a unique combination of a conceptual understanding of a business situation and an understanding of its practical applications. Consultants must have an extraordinary perspective at all levels of strategy, from the most abstract and visionary ideas to everyday things.
Self-awareness is important for consulting firms because it demonstrates the capacity for self-reflection and development to address areas of weakness. You'll likely be asked about your weaknesses, so keep some good and appropriate examples handy. Remember: this shouldn't be too bad, but “I'm a perfectionist” isn't likely to fly either. You can also show that you're self-aware by reflecting on what you've learned in some of the anecdotes you share.
If you talk about your experience as a team leader, end the description with a vision of what you would do differently next time or what you learned from the experience. According to Socrates, wisdom was the admission that you are not wise. Outwardly, you might think that the default position in consulting is for young consultants to pretend that they know everything. This makes sense because the fast pace of work, combined with generous investments in learning and development, allows consultants to quickly develop skills that allow them to work in many sectors performing functions after leaving consulting.