Usually I'd say "don't give up hope" when things are getting tough, but that's wrong.

The only good reason to be hopeful is because things are going well. If someone's had their legs cut off, there's nothing wrong with them feeling hopeless about their situation. Hope is only good in those situations if it helps them feel better, but the reality is that it doesn't and it actually makes people feel worse because now they feel like their lack of hope is a personal failing. The people who are hopeful when things are going badly are deluding themselves. I think that making people feel like they should be hopeful all the time is gonna kill someone, and that's the big con of hope. "Don't give up hope" is what we tell people when we've run out of other helpful things to say. That's not advice. That's a bunch of empty, unhelpful words. The best advice for someone who's going through a rough time is "this is fucked up, and it fucking sucks that it's happening to you, and it's okay to feel like shit about it."