Why is sex a threat any more than an important loving relationship is?
I think the weight that sex carries in a broader society sense has a lot to do with it, so a romantic nonsexual relationship may not be deemed as 'romantic' in general, because there is no sex involved. For some people it's not a 'real' relationship.
What is it about sex and lust specifically, that makes us feel jealous?
We're taught that lust should be channeled in one direction, and not anywhere else. To acknowledge out loud, and accept, that you lust in a broader sense even when you're in a monogamous relationship, is cause for concern because it goes against what we've been taught. You informally give up your right to feel desire towards anyone who isn't your significant other, which might be where the whole "Well, if you still wanna have sex with other people, why are you in a relationship/engaged/married?!?!?! Just be single!" argument comes from.