Looks like I am taking the unpopular view (again). Cough. As a sensitive person myself, I feel like I should try to exlpain that side of things.
But first I want to say that I really despise the word "oversensitive" in labeling sensitive people. It's an insult that tries to invalidate another's feelings. Of course people are free to assign that label if they choose. If they do, though, I generally find the label "insensitive" to be wonderfully handy.
Anyway, on to the actual topic. Or an analogy for it. Or several.
I often help people who are struggling with mathematics. Basic math, algebra, calculus, advanced theoretical courses, lots of different levels. And teaching the actual ideas and techniques is never the hardest part. The hard part is to get the person to let you in enough that they trust you with something that scares them. Some people are so threatened by the subject, it's almost like a small trauma. It's a delicate thing to go in there, and get them to let you lead them through processes that are (at first) terrifying for them.
So. If I'm working with someone who can't even understand basic concepts and struggles with the simplest tasks, and my student of the previous hour was kind of a wiz - I walked them through the whole concept of differential calculus in one session and they didn't miss a beat - what do you think I'm going to do? Is it a good idea to say "Wow, my last student was so sharp - she caught on to all this really advanced material like it was nothing!" The poor struggling student is already feeling shaken and inferior. I'm trying to help them build some confidence. Of course I'm not going to mention the other student's impressive performance.
This is common sense to me. I have learned, by living in the world, that these kinds of things are not common sense to many people. And much like green427 but in reverse, I've found that I need to steer clear of them. To keep myself in one piece.
If there's something I'm really not good at (and there's plenty!) maybe I'm fine with it, maybe I've been able to come to terms with it, or maybe it's a very painful, frustrating, sensitive subject for me. Unless you know me really well, it would be a bad idea to tell me how impressive someone else is at that task. I think the smart and considerate thing is to err on the side of caution until you have a solid sense of where a person is at.
Because relationships (even friendships) are alot like that teaching situation I described. People have painful places. If you want to be their friend, on some level, in some sense, you are asking them to trust you and let them in. That may involve being careful not to hurt them once you get there. And what that means is different for every person, so you have to pay attention and learn. Every time.