Responsibility involves the obligation to answer for actions (the etymology of the word ultimately relates to Latin respondere (to reply).
Generations of worry about a Christian Last Judgement have engrained a sense of "personal responsibility" into ethical decision-making. Any action seen as causing a situation can (in a hyper-critical society) become an occasion for sheeting home "responsibility" (blame).
In politics, calls for responsibility form a pejorative means of attacking political opponents. This habit of demanding behaviour aligned to one's own desires also occurs in other arenas: one expects "responsibility" from children, workmates and employees, meaning they should change their attitudes to suit the speaker.