Exoplanet science is one of the most thriving fields of modern astrophysics. A major goal is the atmospheric characterization of dozens of small, terrestrial exoplanets in order to search for signatures in their atmospheres that indicate biological activity, assess their ability to provide conditions for life as we know it, and investigate their expected atmospheric diversity. None of the currently adopted projects or missions, from ground or in space, can address these goals. In this White Paper, submitted to ESA in response to the Voyage 2050 Call, we argue that a large space-based mission designed to detect and investigate thermal emission spectra of terrestrial exoplanets in the mid-infrared wavelength range provides unique scientific potential to address these goals and surpasses the capabilities of other approaches. While NASA might be focusing on large missions that aim to detect terrestrial planets in reflected light, ESA has the opportunity to take leadership and spearhead the development of a large mid-infrared exoplanet mission within the scope of the "Voyage 2050" long-term plan establishing Europe at the forefront of exoplanet science for decades to come. Given the ambitious science goals of such a mission, additional international partners might be interested in participating and contributing to a roadmap that, in the long run, leads to a successful implementation. A new, dedicated development program funded by ESA to help reduce development and implementation cost and further push some of the required key technologies would be a first important step in this direction. Ultimately, a large mid-infrared exoplanet imaging mission will be needed to help answer one of humankind's most fundamental questions: "How unique is our Earth?"