One of the way I have heard of understanding reactionary political thought is as a response to progressivism. Reactionary position frequently take up the position against some position of progressivism, either through some movement toward a more traditional position or an outright rejection of the progressive position. One way of supposedly unifying the diverse forms of reactionary positions has been to propose that they all reject the idea that all people are equal. This is almost certainly false, but it does give some perspective.
What seems to unify all of this disparate attempts at reactionary politics is that at the base they are philosophically progressive and modern. The idea of progress necessarily involves a moving towards something and a moving away from something. Historically this means moving away from what is old and embracing the new. Scientifically we are moving towards a perfection of science, such as quantum mechanics, away from old out-dated science, such as Ptolemy’s universe. However, in this sense of progress even quantum mechanics will be superseded by something new and different.
The essential problem is that the idea of progress and progressivism themselves have become too old. By their own principles they must be discarded for something more advanced. Reactionarism is then the next step in progressivism itself. In order to progress, we must move beyond progress and progressivism. This naturally leads to the idea of undoing what progressivism has wrought or simply an outright rejection of progressivism.