Dialectical philosophy understands reality and thought as developing through contradiction and its resolution, treating conflict and instability as the engine of change instead of as errors to be cleared away.
A myth has to be cleared away first. Hegel did not use the formula thesis-antithesis-synthesis. The phrase comes from Fichte's vocabulary as popularized by Chalybäus, and applying it to Hegel obscures what he actually described: determinate negation, in which a position generates the specific difficulty that undoes it, and Aufhebung, a resolution that cancels, preserves and raises what it supersedes all at once. The movement is internal to the subject matter and not imposed on it, which is exactly the claim that makes the method contentious.
Marx kept the structure and rejected the idealism, locating the driving contradictions in material production instead of in the development of spirit. What followed was less careful. Dialectical materialism as a codified doctrine owes more to Engels, Plekhanov and Soviet textbooks than to Marx, and its promotion to a law of nature, complete with the transformation of quantity into quality, is the version most often attacked. Adorno pushed the other way in Negative Dialectics, refusing synthesis altogether on the ground that reconciliation is precisely what the world has not delivered.
The standing objection is that the method equivocates. Logical contradiction and real opposition are different things, and a philosophy treating a class conflict and a self-refuting proposition as instances of one phenomenon has made a metaphor do the work of an argument. Its defenders reply that formal logic describes static relations well and processes badly, and that any account of how something becomes what it was not needs a vocabulary for internal tension.