not have the heart
To not have the emotional resolve (to do something); to be unable to do something, especially that which is or seems callous or unsympathetic. I didn't have the heart to tell her that I didn't love her anymore. How could you fire someone the day after their father died? I wouldn't have the heart.
not have the heart to do something
Fig. to be too compassionate to do something. I just don't have the heart to tell him the bad news.