This not getting it thing is silly, so for folks still strugling with this -- let me put it into game world terms.
The Qunari (the 'religion' for clarification purposes) do not believe in having sex for sex's sake. Sex is for procreation. That doesn't mean that followers of the Qun don't form romantic relationships. It just means they don't have sex. In fact, when it's time TO have sex, the Higher ups select a partner for you - you have sex and make babies - and move on. It's a very solid example of a whole society of people who are, for all reasons, asexual. They do have romantic relationships. They don't have sexual ones. The two are separate functions entirely.
Sten is actually a very good example of that. In DAO he can "fall in love" as it were, with the Warden. He will begin to call you Kadan, which is a term of affection literally meaning "of the heart" - aka, someone worth loving. It's separate all together to the term used for non-qun members who are worthy of respect - Basalit-an.
Sten calling the Warden kadan indicates that he has feelings for them beyond just general respect and friendship. The Warden is then someone whom Sten would willingly spend the rest of his days with, even die for. He even goes so far to invite the Warden, a quite literal Bas (outsider) home to Seharon with him. He literally wants to take you home to meet the folks. Even to the point of wanting that he has NO want to convert the Warden to the Qun. Which is probably the absolute biggest indication that he feels more then just outright friendship.
Taking that ALL into account, he still has zero interest in doing the horizontal mambo with them. Not because he doesn't feel romantic feelings for the Warden. It has wholly to do with the fact that the Qunari, by very nature of their philosophy, are an asexual society.
So for ease of wrapping your minds around it - someone who is Asexual does not, at all, need or usually want, to have sex with someone to express their romantic feelings towards someone. That doesn't necessarily mean they wont for the sake of their partner. It just means that they feel that sex is sex (a thing you do to make babies) and romantic love is love. And the two don't at all need to intermingle to have a fulfilling, life long relationship.