Solar Sailing NOT Impossible, But Probably Impractical
Your argument is fallacious simply because it ignores the fact that light pressure is real and easily observed. It produces one of the tails of the comet. (The other is produced by solar wind.)
Here is the source of your error. You assume that light is reflected without loss of energy. This is incorrect. The photon suffers a loss of energy, and is thus reduced in frequency (red shifted). Thus Thermodynamics and Conservation of Momentum are both obeyed.
David F Mayer