Classroom interactions emerging from socioscientific argumentation may be incompatible with the traditional definitions of learning, thus creating tension and potentially undermining its implementation. Leveraging existing literature, we identify argumentative talk that shifts away from scientific content and toward subjective claims, as well as instances of unproductive argumentation as the points of incompatibility. We contend that attention to the degree of compatibility of enactments of socioscientific argumentation with traditional schooling practices may be necessary for substantive implementation. The role of teachers' and students' interactional moves in relation to this compatibility is qualitatively examined using two analytical frameworks related to the content and form of the students' arguments. To generate practical implications with empirical foundations, compatibility is examined in teacher-led and peer-led argumentation. In teacher-led argumentation, we show that the degree of incompatibility can be managed when teachers extend their elicitation of responses with follow-up interrogative questioning, leading students to rely more on scientific knowledge. In peer-led argumentation, incompatibility can be identified when the argumentation collapses into confrontational disagreement or uncritical agreement, obscuring instances in which students rely on scientific knowledge. We discuss the significance of productive talk moves as a way to advance from incompatibility with traditional schooling toward integrating socioscientific argumentation as a core instructional practice.