Don't, just don't. The recruiter has the implicit trust of the company, and you are unknown quantity. If you complain, they will understandably assume the worst about you. Life isn't fair, deal with it. Lick your wounds, come back a year or two later... or apply to another company.

PS: just in case, look introspectively as well. Are you sure it is "the other's fault"?

I am not an expert but am an industry hire who is going for MBB but has the experience of helping my HR recruit new hires as an in-house consultant for some time. I agree with Guennael 300% on firms' granting recruiters/case givers/interviewers with the "implicit trust" on their ability to interview you. If you complain, you not only lose your chance of interviewing there again in the future but also force the firm to remember you with a bad taste. Whoever gave you a hard time might not be working there by the time of your second attempt in few years. We live in the small world, and don't just burn the bridge now for later.

I've been interviewed by a non-MBB consulting firm. I had an incident where one of the managing directors who interviewed me over the phone during the second interview of my round 2 had to hang up on me in the middle of giving me a case because of a client call. By then, I had spent only 20 minutes of the 30-min scheduled slot. Even before reaching out to HR about re-scheduling the call, the firm sent me a rejection email. Was it fair? No. Was I angry? Yes. Did I complain? I did among my friends and family. Did I report to the firm? No. That says something about the culture of the firm, and I stayed away from the company. Looking back, I am so glad that I did.

With that note, yes, life is not fair. Whatever the firm was, that is not the only firm in the world. Stay away, cool off, continue practicing your cases and focus on your career with your goals intact. Just my two cents.

Hi,

I recommend deriving the best out of this feedback and moving forward. You will get literally nothing by complaining and this can even close the future opportunities with the company.

Consulting interviews is a lot about luck and there is nothing you can do here. What you can do - prepare and perform at your best.

Good luck!

Agree with everybody else here: Tough luck, deal with it.

And by the way: Clients will be d*cks and c*nts as well sometimes. So get used to it. It happens, there's no way around it. Best you can do is stay the course and make them regret they didn't hire you by being awesome somewhere else.