Counterspeech, i.e., responses to counteract potential harms of hateful speech, has become an increasingly popular solution to address online hate speech without censorship. However, properly countering hateful language requires countering and dispelling the underlying inaccurate stereotypes implied by such language. In this work, we draw from psychology and philosophy literature to craft six psychologically inspired strategies to challenge the underlying stereotypical implications of hateful language. We first examine the convincingness of each of these strategies through a user study, and then compare their usages in both human- and machine-generated counterspeech datasets. Our results show that human-written counterspeech uses countering strategies that are more specific to the implied stereotype (e.g., counter examples to the stereotype, external factors about the stereotype’s origins), whereas machine-generated counterspeech uses less specific strategies (e.g., generally denouncing the hatefulness of speech). Furthermore, machine generated counterspeech often employs strategies that humans deem less convincing compared to human-produced counterspeech. Our findings point to the importance of accounting for the underlying stereotypical implications of speech when generating counterspeech and for better machine reasoning about anti-stereotypical examples.