First you have the combination of a rotating airfoil with more air speed on the "leading" edge of the air foil and less air speed on the trailing edge of the air foil. Depending on the airfoil shape, this could cause a direct rolling torque, that would result in a pitch reaction.
In addition, the boomerang may produce more lift at the "front" than at the "back" (or vice versa) and the pitch torque would result in a roll reaction.
Depending on the design, and given enough altitude, a boomerang will fly in a figure 8 pattern, although if through from the ground, many designs will land before making the transition to the second half of the figure 8 pattern.
The Aerobie flying ring is a special case. There's very little different in lift between the left and right side, or the front and back side, allowing an Aerobie to fly without the normal precession effects you get from boomerangs or frisbees. An Aerobie is best thrown with no perceptible angle of attack, relying on the airfoil's special shape to generate lift. It will actually climb without changing pitch if thrown horizontally with sufficient air speed, most noticable if it flies into a gusting headwind.
Link to boomerang web site (earlier chapters have some generic stuff about aerodynamics): boomerang5.htm