This paper discusses the potential role of fossil natural gas in the process of the energy transformation in Europe on its way to decarbonization. Mainstream conventional wisdom has it that natural gas, perhaps in combination with other gases, should maintain an important role in the energy mix, first, as a "bridge fuel", and then through a gradual transition toward "decarbonized gases". However, when considering the ambitious climate targets of the EU and the subsequent need for far-reaching decarbonization, in combination with technical constraints and the results from our own energy system modeling, we arrive at a contrasting result: The disappearance of fossil natural gas and its corresponding infrastructure is the next logical step of the transformation process in Europe. The paper provides a review of the issues at stake and deconstructs the dominant narrative through a detailed technical description of different energy gases and their real climate effectiveness, as well as results from energy system modeling. We conclude that the phase-out of fossil natural gas in Europe needs to be completed towards 2040 in order to comply with climate targets and provide planning reliability for policy-makers and the industry.