Should we really be trying to be less offensive, or less offended by things?

Both. If you know you are offending someone by saying something mean, maybe you shouldn't. It creates unnecessary tension (not only on the other person but also on you). If, however, you notice that everything and everyone offends you, perhaps the problem is in you: why do you look so down on yourself? What is the source of your stress and what makes you on defensive mode all the time? Try answering to the root of the question and you will notice that offending someone OR being offended over nothing is just plain useless. The only instance being offended helps is when you are fighting unfairness towards someone else - when you protect. Any other instance seems to create more suffering without solving the problem. We may be total opposites but when there is a problem, we must find a way to come together to solve it.