The networking field has recently started to incorporate artificial intelligence (AI), machine learning (ML), big data analytics combined with advances in networking (such as software-defined networks, network functions virtualization, and programmable data planes) in a bid to construct highly optimized self-driving and self-organizing networks. It is worth remembering that the modern Internet that interconnects millions of networks is a `complex adaptive social system', in which interventions not only cause effects but the effects have further knock-on effects (not all of which are desirable or anticipated). We believe that self-driving networks will likely raise new unanticipated challenges (particularly in the human-facing domains of ethics, privacy, and security). In this paper, we propose the use of insights and tools from the field of "systems thinking"---a rich discipline developing for more than half a century, which encompasses qualitative and quantitative nonlinear models of complex social systems---and highlight their relevance for studying the long-term effects of network architectural interventions, particularly for self-driving networks. We show that these tools complement existing simulation and modeling tools and provide new insights and capabilities. To the best of our knowledge, this is the first study that has considered the relevance of formal systems thinking tools for the analysis of self-driving networks.