Hello,
I'm sorry to hear that you were "counseled out" by BCG, I can only imagine how confused you feel right now. It's important to remember that this doesn't necessarily mean that you aren't suited for consulting, but it may be worth taking some time to reflect on your experience at BCG and identify any areas where you could improve. In my opinion, this is the number one priority for you: to understand what happened and use this knowledge in your advance. As if you have a rejection during the interview process with BCG and an upcoming interview with McKinsey. Using the feedback from the first could help you succeed in the latter.
When applying to other consulting firms you -again in my opinion- shouldn't mention the fact that you were “counseled out”. You could apply for a different location and say that due to personal reasons you needed to change city or anything else like that.
BUT if they ask you specifically about this and you choose to be honest it is important to be transparent and at the same time frame it in a positive way. You could explain that while you had a challenging experience, you learned a lot about the consulting industry and have identified areas where you could improve. You could also emphasize any successes or accomplishments you had during your time at BCG, such as completing a project or receiving positive feedback from clients.
In addition to applying to other consulting firms, you may also want to consider other career paths that align with your skills and interests. Consulting isn't the only industry that values analytical and problem-solving skills, so it's worth exploring other options as well.
Ultimately, it's important to stay positive and persistent in your job search. Rejection is a natural part of the process, but it's important not to give up and to keep working towards your goals.
Good luck!