Eden wants him to love her and she wants to 'do her duty' to God.
I feel for her because she's young and she's been brainwashed and kept ignorant, and she has no idea of what real relationships and love are.
I imagine there are a lot of young brides in Gilead feeling that way. Confused about why their husbands don't love them and why their marriage hasn't made them happy when it's their purpose.
But she's going to be a living nightmare because of her ideals, and I think she might be spiteful.
She's either going to report Nick because she thinks he's a traitor (gender or otherwise) or go after June when she realises Nick loves her, because she will think with June out of the way Nick will learn to love her.