As with most aspects of aerodynamics, adverse yaw can be explained in many ways. Different ways appeal to different listeners, but all of the useful explanations (at least appear) to match the observed effects.
Some people explain adverse yaw in terms of the different pressures above and below the wing. Pressure is higher below than above. So the down-going aileron is acted upon by comparatively high pressure, while the up- going aileron is acted upon by a lower pressure. This causes more drag on the down-going aileron, so the aircraft yaws away from the roll. The problem with this explanation is that it appears to ignore Bernouli's argument that total pressure is constant.
More significantly perhaps, dynamic pressure, which only acts downstream is greater in the high speed flow above the wing. So the up-going aileron should produce more drag...but it doesn't???
Another explanation is based on changes in the relative airflow and the effects of these changes on the direction of the total aerodynamic reaction generated by each wing.
Total reaction does not act at right angle to the relative airflow, nor at right angles to the chord line. But its angle is dependent upon both of these. When an aircraft rolls, one wing goes up and the other goes down. Let's assume (as a starting condition) that the relative airflow is horizontal and the total reaction is at an angle of 110 degrees above the relative airflow. This means that the total reaction is angled 20 degrees rearwards. And for the sake of simplicity let's assume that the angle between relative airflow and total reaction remains constant (yes I know it won't really do that but let's try to keep it simple).
The up-going wing (with its down-going aileron) experiences a downward airflow. This tends to tilt its relative airflow downwards. If the relative airflow tilts 10 degrees downwards, then the total reaction will now be at a rearward angle of 30 degrees. This reaward tilting of the total reaction will increase the drag. The down-going wing (with its up-going) aileron experiences an upward flow. This tilts the total reaction in a less rearward direction, thereby reducing its drag. So the aircraft yaws away from the roll.
Readers may of course pick holes in this theory, and could (and probably will) come up with other explanations.
Personally I prefer the argument that the Pink Pixy likes to keep us all guessing.