You guys are assuming what she said was true but it might not be. I’m not necessarily calling her a liar, i’m just saying her view of the situation (whatever it is) is probably biased.
Personally, I don’t think she was telling the truth about Henry’s father to Mary Margaret. I think there is more to the story that Emma doesn’t want Henry to know about his father and herself. I always thought she could be lying about him because if she was telling the truth about him, why did she keep his car ( unless it was stolen when they met ).
To me that is another question with Henry’s father and Emma:
If Neal is the father than why did she keep the car.