It's a lengthy article aimed at therapists, but there is good advice here for parents. The part I found most concrete was how to respond to "I hate everybody!"
... I suggested she might respond with something like, "Yeah, I think I have days when I hate everybody, too" or "What was your day like that you ended up feeling like you hate everybody?" or "How long does your 'I hate everybody' mood usually last?" all asked sincerely, not somberly as if trying to ferret out an underlying pathology. These questions would assist the counselor in joining Elise by normalizing what she felt instead of turning it into something "bad" or abnormal. Moreover, such responses would prevent conversational shutdown by communicating, "Yes, I understand how you can feel that you hate everyone in the world, and maybe today--or every day--you do. But nothing about that keeps us from talking about ways to help you make it through the school day."