Raw grief- Kishimoto has shown us before he has a sharp understanding of what that can do even to the strongest person
Tsunade over Nawaki and especially Dan, with Jiraiya she was initially more in control- having dealt with this kind of devastating blow several times before, we haven't seen her direct reaction to Hashirama and Tobirama's deaths, plus she would have been really young when they both died, but it left her with a lasting bitterness. But even with Jiraiya's death we see a bit of grief rage- she basically tells Ibiki he can do the harshest torture, basically sanctioning even torturing to death, on that Rain ninja Jiraiya captured- cold blooded violence, something Tsunade would otherwise oppose, but her raw grief anger overwhelms her usual nature.
Naruto- feeling driven to want violent revenge by his raw grief over Jiraiya's death, something he has to overcome.
Sasuke- basically driven to complete psychosis by his unending grief anger.
Shikamaru- raw grief anger drives him to plan a suicidal attack on Hidan and Kakazu. He's so far gone into it that he doesn't realize it's a suicidal, and convinces his grieving team mates he has a valid plan.
Nagato as well, his raw grief over Yahikko's death breaks his soul...
People do things during raw grief that they'd not otherwise do- and suicidal acts and thoughts are very common. Even Yoko Ono admitted her first reaction when the doctors told her they couldn't save John Lennon's life, was wanting to die herself. It was only seeing her son Sean's (then just 5 years old) reaction to learning his father had been murdered by an insane person (he was told the next morning), that made her decision to stay alive for her son.