1 general:: Phrase(s): 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.
McGrawhill's American Idioms And Phrasal Verbs
2 general:: Be unable to bring oneself to say or do something, as in He didn't have the heart to tell her the cat had died. [Mid-1600s] Also see HAVE A HEART.
American Heritage Idioms