Calling someone oversensitive is often said by someone who has been insensitive and doesn't want to admit fault or accept blame.
Think about if you are designing a bridge. You wouldn't say that bridge is "superstrong." It conveys no real meaning without some sort of context. Saying, "that bridge can support 16 Sherman tanks driving 30 MPH and will last for 100 years with no maintenance" begins to have some meaning. It has specificity and calibration.
Even with some types of comparatives it is less judgmental and more factual. For example, "you react stronger to criticism than anyone I know" might hurt, but at least there is some calibration. I am not saying it is ever a good idea to give someone this kind of feedback or advice, but at least in might be a true statement. Saying that someone is "oversensitive" is practically false by definition because there is no standard.
I think it is also potentially ok to say something like "you are too sensitive to have the type of job where you have to deal with complaints." Again, a person may not want to hear it, but at least there is something to measure against that can form the basis for a discussion.
Feelings are facts.
If someone is hurt by your remarks, the best path forward is to acknowledge the feeling, apologize, and move on. I believe that some people also use false claims of being hurt, but I suspect that those are relatively rare.
Don't say, but I was only... Don't make excuses. Intent matters, but later, once the hurt dissipates. All this assumes that you care about the relationship of course.