Sensitivity is probably the most common word in the management of relationships. The usual implications is that men lacking it, or even don't have it, are the reasons for social ills. Often men are not even aware that they are hurting. I googled a few sites on this topic and compiled certain things to note, or should I say useful.
If women were to really get sensitive to their men, most often they would be so much disappointed. The men would be thinking, "Why should I be so sensitive? Why do I want to let it affect me badly?". More often than not, when being commented on insensitivity they would think otherwise and goes: "I'll see what I can do and show just how sensitive I can be." Instead, it would probably be more effective that a man needs to regain his sensitivity for completeness, to get out of anger traps, to avoid emotional crippling of both parties, to improve his relationship with a woman, and to rid himself of addictions or to reduce stress.
Men tends to have the capacity to forget things, let go of problems more easily. The only drawbacks of that talent is that it brands us as being insensitive in the eyes of the females.
We are all insensitive in some degree, because your experience is not mine, nor mine yours. Our differences in life experience will cause others' reasoning, ideas, and problems. Instead of demanding total sensitivity, the key is to not respond unhappily when we are misunderstood.