I don’t think you have an underlying psychological problem. I think you are trying to find a rational way to deal with an irrational problem. Clearly, the situation has nothing to do with you. I don’t know what the minister is trying to do. It does seem like he doesn’t necessarily want top students to get into top jobs. This has to be very, very frustrating and discouraging and angry-making.
The only way to manage it, I think, is to tell yourself that, yes, it is all unreasonable but that you still have to do whatever it is that you have to do to pursue the profession you want so much. Remind yourself that the situation isn’t fair, but you have no power to change it. You have to just follow the rules to get where you want to go despite the unfairness.
Then do what you’ve always done successfully. Study. Take the exam and get your usual top score. One of my favorite quotes is by George Herbert, a 16th century English poet and writer. He said, “Living well is the best revenge.” In your case, showing them what you are capable of is your best revenge on an unfair system. Hopefully, once you are in a job, you’ll gain some authority to make changes that will benefit the people coming after you.
I wish you well.