Can you read between the lines? Have you sense the conflict? Are you aware of the real thing? There are arrays of ways to rephrase it but i guess the real question is "how sensitive are you?".
I laid the reversed question to one of my colleagues. "Would you consider yourself as someone insensitive?. He responded with another question "Who would admit he is?". By then i got what i need to hear followed by stories on the surface of his six months relationship with his girlfriend.
"I'm average, i can be sensitive and insensitive if necessary" he continued.
"Necessary? what does it mean? a sound of puzzled from me.
"I tend to be insensitive when i want my girlfriend to realize things, we have issues just cycling around. Whenever i act as if i don't care, she stopped.
I giggled with his answer, it was so real but i told him that won't always work.
I always believe that there's no such person as insensitive, everyone knows. They just prefer to be in the zone of silence, fear of making the initiative, maybe afraid of confrontation or keeping themselves from dreaded reality and making insensitivity as a form of denial. Through my personal experiences and people involved, that belief i reared with to be a fact turned out to be just a mere opinion.
Not all people are good in distinguishing non verbal cues. Not all can reach the core of each or anyone's emotion. Not all care about, not because they literally don't care but because "they don't know". Funny for me to know but yes, they just "don't know".
Let's take the worst scenario. In psychology, we call them alexythemic, people who are emotionally tone deaf. They can't distinguish their own and anyone else's emotion, because of that, they're having a hard time expressing themselves. Ridiculous isn't it? (am afraid, i belong, haha). Imagine yourself crying after watching a movie and when asked what particularly made you cry, you don't know what to say and you can't even justify the feeling. They are emotionally dysfunctional. For me that's more than insensitivity.
Since human have this gift of emotion incomparable to any living animals, we should be thankful that we "feel" and it's great that in any way we "show". We just have to remember that emotion is essential to action and action is essential to emotion.