Can't comment on the birth control, as my SO and I don't have any need or it.
On the desire thing, though, I kinda agree with you. You want her to want to have sex and for her to enjoy it. This shows that you care for her, which is a good thing, and is far from universal among men or women. Of course we want our partners to want to have sex with us; it makes us feel desirable. And it is much better when both partners are really into it. Doing it just to please your partner once in a while is fine, but having sex solely for that reason can lead to an unfulfilling sexual relationship for both partners; I've been in one of those, and it didn't work out in the long run.
But I'd also say that until you figure out a solution to the libido problem, accept her at her word when she says she's happy to have sex with you because it makes you happy. You're making her feel desirable, and she's getting some pleasure out of pleasing you. Vicarious pleasure is better than none.
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