In this position paper, we advocate for the development of conversational technology that is inherently designed to support and facilitate argumentative processes. We argue that, at present, large language models (LLMs) are inadequate for this purpose, and we propose an ideal technology design aimed at enhancing argumentative skills. This involves re-framing LLMs as tools to exercise our critical thinking skills rather than replacing them. We introduce the concept of \textit{reasonable parrots} that embody the fundamental principles of relevance, responsibility, and freedom, and that interact through argumentative dialogical moves. These principles and moves arise out of millennia of work in argumentation theory and should serve as the starting point for LLM-based technology that incorporates basic principles of argumentation.