The potential effectiveness of counterspeech as a hate speech mitigation strategy is attracting increasing interest in the NLG research community, particularly towards the task of automatically producing it. However, automatically generated responses often lack the argumentative richness which characterises expert-produced counterspeech. In this work, we focus on two aspects of counterspeech generation to produce more cogent responses. First, by investigating the tension between helpfulness and harmlessness of LLMs, we test whether the presence of safety guardrails hinders the quality of the generations. Secondly, we assess whether attacking a specific component of the hate speech results in a more effective argumentative strategy to fight online hate. By conducting an extensive human and automatic evaluation, we show how the presence of safety guardrails can be detrimental also to a task that inherently aims at fostering positive social interactions. Moreover, our results show that attacking a specific component of the hate speech, and in particular its implicit negative stereotype and its hateful parts, leads to higher-quality generations.