When someone attempts to make you responsible for their feelings, they are committing what psychologists call emotional blackmail. A parent uses this when he or she tells a child, "You've hurt me so much" or when a spouse says, "You hurt my feelings."
It is placing responsibility for their emotional outcome on you--pretending you have control over something you do not. The parent may choose to become angry or sulk or become bitter or irritable toward the child. Someone may claim your action justifies their emotion. But that person is still doing the choosing of their own emotions.
When you see a family tiptoe around the house because "we don't want to upset mother (or father)" then you have a family who has decided to make everyone responsible for a single person's feelings--taking on a burden they were never meant to carry. Each family member is responsible for his or her actions. To make preventing someone from being upset a goal is wrong.
Elizabeth Kenny once said, “Anyone who angers you, conquers you.” To allow someone else to decide how you feel is abdicating your responsibility to define yourself. Don't allow someone else to sell you on the idea that you are responsible for what they feel. And don't blackmail those around you by threatening to unleash an emotional outburst over something you are blaming them for creating.. when you did that yourself.