To be fair, Emma did not want to get involved in Henry’s life because she did not think she was good or him–she had good intentions for him. She only got involved when she saw how Regina could be harsh to him–and she could be. 🙂
And Emma has never put Henry in danger–I honestly cannot recall any scene where she endangered his life or hurt his feelings, other than trying to take him out of Storybrooke. 🙂 Regina tricked Emma into saying how crazy she felt the curse was in front of Henry hurting his feelings. She got Archie to tell Henry that his claim was crazy and a delusion, which also hurt his feelings. He said so himself that she made him feel crazy. She kiled Graham, causing Henry to feel fear and guilt over the Graham’s death, along with thinking that Emma could be in danger.