Empirical observations trump theory. Theory is an attempt to explain how the universe works, but it does not dictate the universe's workings. Grad-level physics can explain why the EM Drive shouldn't work. Newtonian physics can explain why GPS shouldn't work, too; and yet the accuracy of the results remain as high as ever.
The problem is, according to everybody who has tested it, the EM Drive does produce thrust. When your theory contradicts reality, it is the theory which is discarded (or at least updated). Unless there's some pervasive experimental error in all of the independent observations of this effect - which is possible, but becomes less likely with each successful reproduction - that will need to happen with our understanding of those grad-level physics you studied.
In that case, on your final, you did the equivalent of computing that if a 1kg object (constant mass, initially at rest relative to you) produces 10^8 N of thrust in a straight line away from you for six seconds, it'll be going at just over twice the speed of light relative to you afterwards. Perfectly consistent with physics as it was near-universally understood until 110 years ago...
Of course, in this case, we have an experimental result before we have a fully consistent theory to explain it. In a reversal from the way much (though not all) recent physics progress has been made, the empiricists appear to be outracing the theorists. That's why right now there are a number of hypotheses, each of which have problems. More experiments will allow us to refine those hypotheses and throw out those which are shown to be incorrect (for example, Guido Fetta - of the Cannae Drive - had a theory that radial slots inside the drive's chamber were required; NASA demonstrated that they weren't). More time will also allow theoretical physicists to work out the underpinnings of how this happens. That will expand our understanding of the universe, give us the tools to predict future experimental results (rather than trying to explain the result after the fact), and open new branches of scientific exploration.
The above paragraph is, of course, predicated on the assumption that the effect does happen. I'm not discarding the possibility of experimental error at this point. It is simply becoming less and less plausible of an explanation.