Labelling an opponent's argument offensive does not win an argument
It is becoming increasingly common to find commentators both on the web and in face-to-face discussion arguing in the following way. A point is made with which they disagree – for instance one critical of religious belief or concerning the definition of rape – and the commentator feels that his or her opponent’s argument can be dismissed simply by labelling it offensive.
What the commentator is de facto saying is that the “offensive” argument simply shouldn't exist. The logic is that if the allegedly offensive argument, which contradicts his or her own views, is taken away, then the remaining argument is strengthened and legitimised. That is not so.
No argument can be deemed illogical, incorrect or morally wrong simply because somebody else finds it offensive. Labelling an argument “offensive” only says something about the people using that label, namely that they don’t like it. It does nothing to qualify or demolish the allegedly offensive opinion.
At one time people found it offensive to suggest that the world was round, or that the earth circulated the sun; their feeling of offence couldn't change a fact. At one time a majority of people found homosexuality offensive, but their bigotry couldn't prevent the development of the idea that human beings, whether gay or not, should have rights.
Nobody should be prevented from saying something simply because someone else finds it offensive. Offensive opinions (and of course they exist) need challenging, but that is not done simply by labelling them offensive.