Is it possible for both sides of an argument to be wrong? Assuming that wasn't a rhetorical question: certainly. That's actually mostly the case, which is also

Is it possible for both sides of an argument to be wrong? Assuming that wasn't a rhetorical question: certainly. That's actually mostly the case, which is also the reason why debates can drag on endlessly, each one pointing out wrong parts in (usually irrelevant) parts of the arguments of the other, while drifting further and further from the original point. If people forget to focus on cooperation and reaching consensus, then constructive discussions are nearly impossible.