emotionally inept 

Someone who has little or no grasp of other people's feelings and/or problems assessing how one should act towards others emotionally.

'He just punched her in the gut and carried on playing without any apology or sign of remorse'
'He's so emotionally inept'

emotionally inept by Clownporn93 November 19, 2013

Emotional Inertia 

The amount of emotional stability associated with an individual as it pertains to how dramatic an event is required to move them to an extreme emotional state.

His girlfriend seems to be able to be moved to tears by such a simple thing as a greeting card commercial. That chick has absolutely no emotional inertia!

Emotional Inertia by SmoovJC November 21, 2012

Emotional inertia 

When something is so emotionally overwhelming that it paralyzes you (emotionally) as though the rest of the world is speeding along and you are frozen. This eventually leads to an emotionally slamming of your mind into the proverbial dashboard of life.

When I saw my beloved husband of 32 years naked in our jacuzzi with that 20 year old, I experienced a horrible emotional inertia. When I regained my senses a week later, I ran over him six times with my Hummer.

Emotional inertia by Tina Ballance December 9, 2008