the word sick is perhaps not the best one to use here, as it has a kind of double meaning
for instance fred and rose west were undoubtedly extremely sick and did some very sick things...but they were not insane and knew what they were doing an did it with carefully planned meticulous intent
that is very different from a woman who has for instance say, post natal depression, is being abused and is in fear for her her kids safety and has eventually cracked, become delerious, hysterical and dellusional, and feels driven to commit a deseparate act whilst in the grip of this temporary insanity
both are clearly sick and have done sick things...but for very different reasons