First of all: Congratulations on passing the first round, that's a big achievement already!
Now let me address an elephant in the room, please.
One thing that I am missing in your question is a bit of self-reflection. Have you honestly asked yourself: What if they are right? What if the fit just isn't there?
After all, your interviewers have seen a lot more people come into the company, thrive there or be miserable there, and leave the company eventually. Thus they have A LOT more data than you do to base their fit judgment on. They may still be wrong, but it's more likely that their judgement of FIT is better than yours.
So please do yourself the favor: Look in the proverbial mirror and try to come up with an honest answer to these questions:
- Are YOU really convinced (based on what data, btw) that you are actually a great fit and that they are just not seeing it, maybe because you didn't find the right way to show it? If so, please proceed and work hard on showing it better in the next round.
- Do you just want to convince THEM that you are a good fit in order to get this job, even if you're not so sure (because you really don't have the data to base this assumption on). If so, think long and hard if you want to go down this route.
This is not to say that you may not be a great consultant. But maybe BCG just isn't the firm for you. And that's totally OK. Better find out now than to enter a job where you may be miserable. Life's too short for that.
So basically don't be that guy who goes off the cliff because he's chasing an elusive price (that BCG job) but forgets to look at the road ahead...
PS: That's a bit a problem with a community like this one. Everybody is so focused on passing that interview, getting that job offer, that few pause to think whether this is actually the right thing for them.