All (known) forces are between two charge carriers: electric charge for electromagnetism, mass for gravity, colour for the strong force, etc. You can use electromagnetic interactions to accelerate mass out the back of your rocket and because of that force symmetry the result is that your rocket accelerates in the opposite direction. You can drop a rock and it will accelerate towards the Earth, but the Earth also accelerates towards the rock. The symmetry means that momentum is conserved. Essentially, in order to change your momentum, you need something to push (or pull) on, thereby changing it's momentum, conserving total momentum.
For a reactionless drive you want to be able to change your momentum without pushing or pulling on anything. That idea has all sorts of problems. One of the proposed mechanisms for the EM drive is that it isn't actually reactionless at all: the asymmetric design of the drive canister causes the microwaves to push asymmetrically on the sea of virtual particles that are always popping up and annihilating. So the drive actually would have an exhaust, it would just be virtual particles that were encountered along the way instead of fuel you brought along.