so they probably are at a point where they can then rationalize out what they may think to be some positive aspects, in their mind, of taking the lives of loved ones with them. They may consider the trauma taking their own life will cause their kids, so they may think they're sparing their kids of growing up with that trauma. Or like what the article stated, it sounds like the doctor knew his kids also had anxiety issues and probably convinced himself he was doing them a service by releasing them from anxiety. Or maybe they think they're doing good to spare their children from ever having to experience the inevitable pains, illnesses, and stresses they would otherwise experience throughout their life, both physical and emotional/mental.
Unfortunately, once they're gone, we can't ask them the real why and then try to offer intervention to get them the help they need.