Previous studies have demonstrated that arguments incompatible with prior beliefs are subjected to more extensive refutational processing, scrutinized longer, and judged to be weaker than arguments compatible with prior beliefs. However, this study suggests whether extensive processing is implemented when evaluating arguments is not decided by argument compatibility, but by congruence between two evaluating tendencies elicited by both argument compatibility and argument quality. Consistent with this perspective, the results of two experiments show that relative to congruent arguments, participants judged arguments eliciting incongruent evaluating tendencies as less extreme in strength, spent more time, and felt more hesitant generating strength judgments for them. The results also show that it is mainly incongruent arguments, not congruent arguments, whose strength ratings were more closely associated with the perceived personal importance of the issue, which intensified the tendency to evaluate arguments depending on argument compatibility. These results suggest that it is the incongruity between argument compatibility and argument quality, and not simply the argument compatibility, that plays a more important role in activating an extensive processing in the evaluation of arguments.