In principle, rectifying phonon and electron flows appear similar, whereby more energy is transported in one direction than the opposite one. However, their physical mechanisms are inherently different. By using molecular dynamics simulations, this study reports on a few interesting aspects of thermal rectification in carbon nanotubes: (1) The dependence of the rectification ratio on the structural symmetry (represented by the position of vacancy clusters) of the nanotube and more importantly (2) a reversal in the rectifying direction as the normalized temperature difference of the heat baths is increased. The flux-mediated diffuse mismatch model is extended to explain the reversal phenomenon—initially with a simplifying assumption that the transmission coefficients at the vacancy/scatterer are identical in bidirectional phonon transport, and then with a moderating factor to distinguish between both coefficients. It is noted that in both cases, the conditions for thermal rectification reversal are attainable and thus explain the results of the simulations.