If we disregard all the other stuff I said, the only things left that I can think of are:

A. You just want to be able to say that the two of you are a couple, despite the other person not wanting to be in a sexless relationship

(Like I said, you don't have to be "going out" with the person in order to gain their affection. What you're looking for is close friendship. It holds all the benefits of dating without sexual expectations. Let go of the labels, they're holding you back from feeling happy with what you have)

B. You like them so much that you wish you were able to become sexually attracted to them even though you just can't

(I get that you want to feel closeness with the person, but being in a relationship with them isn't the be-all end-all, nor is it the only validation of feelings between two people. Or is it because this person wouldn't like you as much without sex? If that's what the person really wants out of you, than their feelings aren't true in the first place.
Save your affection for someone who likes you for who you are)

C. This whole thread is a public scapegoat explaining how you "like the person" but aren't gay so you can't be with them, so that you don't hurt their feelings and they'll understand through the reading of other people's opinion on it

(If that's the case, me putting it out there as a possibility isn't helping at all lol)