If someone says they " don't have the heart to do (something)" they mean they don't want to say something or do something because they think it will hurt another person's feelings – it will make that other person feel bad.
如果有人说他们“不忍心去做(某事)” ,他们的意思是他们不想说某事或做某事, 因为他们认为这会伤害他人的感情——这会让对方感觉不好。