Law is the study of causation, proximity and effect. The duty of care
arises from the legal concept the neighbour principle. Who is my legal
neighbour? They are the persons that are or ought to be in my
contemplation when commiting acts or omissions.
An insult, particularly if objectively considered to be an insult, can
of course lead to legal consequences. An insult on the grounds of race,
colour,creed, gender and so on can in particular can lead to civil
and/or criminal liability on grounds of racial or sex discrimination.
But it depends on context. You go out into a field far out in the
country in the dead of night. You say out loud "these dammned blacks /
women / chinks / gays etc.... are taking our jobs!" unlikely to be
prosecuted as no legal neighbour around to raise a question of legal
wrong in law. On the Other hand: you go to your place of work and say
the same thing. Much more likely there may be some legal consequences.
But what if the place of work involves repairing computers and the only
words used are "chink" or "chinks" to describe the origin of computer
parts? And the only people there are all of the same ethnic and national
origin. None are of chinese origin. Nobody takes offence. It would take
someone to take offence and report it I would have thought in order for
legal consequences to follow. For a criminal case there would have to be
some evidence of intent to breach the peace or unlawfully discriminate.
Without evidence of a legal neighbour that the speaker of alleged
offensive words knew or ought to have known would be offended, then it
could be rather more difficult to prove intent.