Offense = Harm

Only if a statement that causes offense is false, can it be harmful, and perhaps not even then. Having hurt feelings and being harmed ate two separate things. Having your feelings hurt can actually be helpful, rather than harmful. If the charge against you is true, then you can use it as a catalyst for self-improvement. If it is false, there is no cause for offense in the first place. 

I can't even think of an example of someone saying something that causes offense, in which it is justified for the recipient of the critique to feel offended.

False statements can and do cause harm, but even true statements can be harmful depending on how they’re delivered. This isn’t just opinion, psychology and sociology show that words affect stress, reputation, and relationships in real, measurable ways. Offense isn’t imaginary... it points to underlying harm that research and law both recognize. That’s why claiming offense is never justified ignores science, history, and human experience.

Sources

Teicher, M.H., Samson, J.A., Sheu, Y.S., Polcari, A., & McGreenery, C.E. (2010). Hurtful words: Association of exposure to peer verbal abuse with elevated psychiatric symptom scores and corpus callosum abnormalities. American Journal of Psychiatry, 167(12), 1464–1471.

I stand by the claim that offense is never justified. I can do this because it can be shown that to not be offended by what someone else says in never necessary, nor is it ever the best response.  So, while I don't deny that people do feel offended, or even that it is a natural response, it is the responsibility of the party receiving the critique to control his own emotions.

I can agree to my opponent's definitions of "offense" and "harm," and also appreciate their granting the fact that I am not referring to physical offense, without my specifying it.

I also failed to specify the exceptions of libel and slander from my statement concerning even false offensive statements not necessarily being harmful, so i must concede that point. However, outside of those two exceptions,  i stand by my statement. I want to remind my opponent that the prompt was not that offense can not be harmful, but that it does not necessarily equate to harm. 

The example my opponent provided of public humiliation by a teacher is a strong one for their position, but even in this case, for the student to be offended, though instinctual and natural, is not the best reaction for the student to have, (though especially difficult to overcome, given the authority/subject dynamic, the perhaps old/young dynamic, the presence of peers, etc.) The student would be best served by prioritizing logic and reason over emotion, and making the following assessments of the situation: Was the critique given, whether kindly or cruelly, accurate, and to what degree? If it was inaccurate, what defense might he give on his behalf, to the class, if permitted, and to his peers privately, if the teacher is truly being cruel? If it was accurate to some degree, or in whole, though embarrassing,  what might he want to change/improve, or what mitigating factors might he wish to voice? He can also make a judgement about the rudeness of his teacher, or the impressionability of his peers, etc. If the teacher was trying to be rude or cruel, and was making an ill-founded critique,  he mustn't give it much weight. He can simply tell himself, "Wow, that teacher is an idiot and a jerk." He can feel free to express these sentiments to his peers, minimizing his embarrassment. So while we would all forgive and understand the young student in this example being offended, we can also see that it isn't the most rational, logical,  or beneficial reaction he could potentially have. 

You'll note that I have no sources as I am relying solely on my own logic, reason, and observation here, but I'm not asking that my opponent follow suit.

I notice that my opponent  is engaged in a different debate at this time, which is perhaps more interesting to them. Thusly, I am uncertain as to where to go from here. I'll conclude by stating that, unless my opponent can show that offense necessarily equates to harm, they have failed to meet the requirements for upholding the statement, "Offense = Harm."