Whether a centralized, distributed, or decentralized system approach is selected for Internet-based services affects sovereignty and responsibilities of users and providers alike. Therefore, computer science education can contribute to informed decision-making and citizenship education by teaching power structures of and responsibilities in digital infrastructures. In this practical report, we focus on the example of instant messaging. We analyze three different algorithms for instant messaging that vary in their degree of (de-) centralization. Based on the analysis, we propose a teaching activity called Klemmchat using the concept of computer science unplugged to educate students on the discovered key aspects and trade-offs. We report on results obtained by teaching Klemmchat in two classes in grades 11 and 12. The evaluation shows that the activity is suitable for conveying trade-offs and helping students to engage with the topic. The results, however, leave open whether the acquired understanding affects usage decisions.