You act. But you don't care about the effects of your actions. That's insensitivity.
Sensitivity means feeling the emotions in the other person when you act. The sensitivity needs to measure only that are you hurting someone. Some people say they don't care if they hurt others as long as they are doing the right thing. So can we call that doing the right thing in a wrong way ? It would be interesting to note their answer to this.
Whether you accept it or not, in reality, karma ensures you have perfect accountability to your actions. You can't escape even if you wish.
Next time when you act, be prepared to answer when someone asks. Just as you have a right to act, they can ask. Then you need to answer. Our social settings do not have an ignorance or exit clause.
Be answerable to your actions.