It's interesting to me that anyone raising a child wouldn't want to be considered a parent. Is the use of this term by request of people actually in this position, or wasn't created by third parties in an assumption that we shouldn't call them parents?
Caretaker and legal guardian have different and more specific meaning than parent. Those terms are needed to more clearly describe a person's situation and involvement with someone else. Again its interesting to me that one would prefer not to be called a parent when they have taken on the responsibility and roles of being a parent to a child.