The “fight fire with fire” adage may have its place in some arenas, but it certainly doesn’t work in the social media management realm. Negative comments are going to occur if you manage a brand’s social media presence. That’s just a fact. However, your response will likely determine whether the issue remains a small blip, or snowballs into a full-fledged viral debacle.
The cardinal sin of responding to negativity, specifically on Facebook and LinkedIn, is that you cannot delete the comment. There are instances where deleting a comment would be appropriate—if personal information or inappropriate language is used, for example—but in those cases you should still reach out to the user directly.