When describing people, someone "sensitive" is usually in tune with others feelings. They are observant of the gestures and facial expressions of those around them. Unfortunately, this can lead to misunderstandings.They might misjudge the meaning of something that was said, overreact to a look on someone's face. They might then be described by others as"hypersensitive", sensing ill will or criticism when it wasn't intended. They would be easily offended. Someone "insensitive" might be described as tactless and unfeeling. The would say things without considering others feelings or culture. They would not be considerate of others emotions. Hope this helps

I would say "heartless" or "cold-hearted". For an extreme, "psychopathic" might be appropriate. Psychopathy is a mental disorder where the person can't feel empathy.

Heartless Cold Unfeeling Insensitive Numb Impassive Thick-skinned

Creo que seria insensible [emoji]