The operations of the Language Faculty generate the asymmetrical structure of linguistic expressions, which provides the spine for their compositional semantics. Neuroimaging results support the structure dependent sensitivity of the brain to language processing. Psycholinguistics results on language development in the child show that language learning is structure dependent and not based on extensive training on data sets. We contrast this view of language computation and learning to Deep Learning, which is claimed to provide the best solutions to many problems in image recognition, speech recognition, and natural language processing. Firstly, we present evidence that the human capacity for language cannot be equated to other cognitive capacities. Secondly, we argue that efficient Natural Language Processing should integrate asymmetry based parsers and we point to shortcomings of Deep Learning approaches to sentiment analysis. Lastly, we draw consequences for models of natural language processing where natural languages are not reduced to data sets.