The right to "Freedom of Speech" is not an unfettered right; one can't stray in to the territory of "Hate Speech" and get away with it by appealing to one's right to "Free Speech" but there are situations where freedom of speech crosses some undefined boundary where the speech may be offensive albeit not in the domain of hate speech.
I might be making a generalization but I think that I am on pretty safe ground to say that we have all been offended at some point in our lives by what others' have said or done. To go on the offensive is to attack someone or something and to take offense is to feel that one is being attacked for some reason. It seems to me that we take offence in at least two different senses; the one is that something is perceived as a personal offense and the other where we take vicarious offense i.e where we ourselves are not the target but we empathetically take offense on other's behalf. I am of the view that taking offense is an intuitive indicator that something isn't right in the world and that this can or should serve as motivation to correct whatever is wrong so I think that "offense" is an important barometer that we should take note of but like many good things, it can be misunderstood or even abused.
Offense isn't an argument, it is an emotional reaction to a situation that is experienced. In some cases the emotional reaction can be justified by reasonable arguments whereas at other times, I think, the reaction is unjustifiable. The right to "offense" is similar to the right to "freedom of speech" where it is not an unfettered right but drawing the boundary between justified and unjustified "offense" taken, like that of "freedom of speech" uttered, is a difficult line to draw. It is like "offended" and "freedom of speech" are opposites but somewhat related where "offended" is a reaction to the action of "speech".
People take offense, ideas aren't capable of taking offense. So for example if someone was to say that "The theory of evolution is stupid" it is never the case that "The theory of evolution" takes offense; if any offense is taken it may be by someone for whom the "Theory of evolution" is true and perceives the statement "The theory of evolution is stupid" as intimating that they themselves are "stupid" for holding that position. This, for me, is a mis-fire of vicarious offense where we confuse ideas and people thinking that ideas, like people, can take offense. In this particular example the statement itself is an issue which highlights how we have a tendency to anthropomorphize many things which I think is the key to understanding what is going on. The "Theory of evolution" can't be "stupid" nor "clever" because those adjectives are used to describe degrees of intelligence which requires the ability, in some form, to think.
Could there be a general rule as to when it is justified to take offense as well as when it is unjustified? When a viewpoint is expressed it seems too easy to claim that "I'm offended" by what has been said and thereby effectively censoring or limiting "freedom of speech" behind a wall of, possibly sincere, but faux offense. One should not be limited in what one is able to say simply because someone else may take offense. Since offense taken can often be expressed as anger I think that working out whether an offense taken and the ensuing anger is justified or not is an important topic for discussion.
Breaking offense down into a few sub-categories where offense is taken to try to tease out when taking offense is justified or not. Is offense being taken :
1.2 Something that a person has chosen e.g. political, religious or other views. If one has chosen a viewpoint to hold then one has some kind of responsibility for holding said viewpoint so if someone else is exercising their right to freedom of speech and without straying into 1.1 and one feels offended, it is time to examine why one actually holds these viewpoints. Being offended is a barometer and sometimes that barometer is saying that possibly your own viewpoint is wrong rather then the argument put forward by the interlocutor. Because we never like to be wrong we all tend to fall back on offense as the defense and as Archbishop Desmond Tutu said when quoting his father who apparently said, "Don't get angry, improve your argument!".
2.2 Concepts, ideology or anything other than a person. This, I think, is mis-firing vicarious offense mistakenly taken up on behalf of something which cannot take offense. In this case it is likely that one is actually in the domain of 1.2 and the barometer is indicating that maybe one should improve one's own arguments rather then being offended by others' arguments. An example of this would be "Blasphemy" where someone is offended on behalf of a god, which by definition, isn't a person so what is happening is that one is taking offense simply because someone else holds a viewpoint different to one's own.
Update : The term "vicarious offense" was suggested by P.K and I have made use of it.