have the heart (to do something)
To be hard hearted, callous, or unsympathetic (enough to do something); to have the emotional resolve (to do something). Usually used in the negative. How could you have the heart to fire Joanna the day after her father died? I didn't have the heart to tell her that I didn't love her anymore.
have the heart
be insensitive or hard-hearted enough. 1990 Neil Bissoondath On the Eve of Uncertain Tomorrows Miguel doesn't have the heart to force her to do what he knows she should be doing.