Over fifty years after its inception, Generative Grammar (GG) has asserted itself as the mainstream theory in neurolinguistics. Countless scientific papers, books, and university departments in their entirety take for granted the plausibility of GG as a biological model of human language, hence committing their research efforts to establishing the neural substrates of generativist constructs. However, several arguments have been set forth against the neurological plausibility of this theory. GG is an analytical theory characterizing structural properties of several grammatical constructs without considering biological data. At the same time, the theory upholds the a priori assumption that such abstract descriptions represent the neurological reality of the linguistic system. Yet, a number of theoretical incompatibilities become apparent upon testing some crucial generative theses against psycholinguistic, neuroscientific, and evolutionary evidence. In this sense, the purpose of this paper is to summarize part of the multidisciplinary evidence casting doubt on the neurological plausibility of GG as regards (i) its conception of linguistic entities, (ii) its defense of syntactocentrism and the thesis of non-redundancy, and (iii) the alleged evolution of Universal Grammar. By way of conclusion, it will be suggested that Generative Grammar is not the most fruitful linguistic theory for the progress of neurolinguistics.