I cannot help but wonder if that's not quite what Stephen Fry said. Being offended is a fact of human life, and saying being offended has no meaning is like saying being upset if your mum dies has no meaning.
The relevant issue is what you do with being offended, and the magnitude of the offence. In many cases for minor issues or harmless disagreements, just deal with it and move on. It will in many cases be appropriate to react, usually by politely informing the person of your disapproval and, where necessary, informing them that you'd like them to stop. And finally, of course, we're often offended because someone has done something with a high potential of harm to others, and even stronger measures are justifiable.