Asymmetric structural representations and operational modes have played a long-standing dominant role in the study of generative grammar. However, symmetry, as a law of nature, has not attracted much attention in the construction of syntactic theories. Starting with the natural attribute of languages, symmetrizing syntax places emphasis on the symmetry of structural representation and syntactic computation, which offers a new paradigm for the study of generative grammar. This paper covers the details of the theoretical origin, basic viewpoints, operational modes and theoretical innovations of this forefront theory of generative grammar and offers a scientific evaluation of the theoretical value and inadequacy of this theoretical framework. In addition, this paper shows the latest development of generative grammar and provides a reference for the study of generative grammar.