I've read through all the replies, sorry that I cannot answer every one separately. As expected, there was a real mix. Some posters assumed I'm a journalist or student - wow that's me rumbled.
Others assumed I'm the man in the hypothetical situation, and proceeded to bully me, because obviously if we're not having sex it must be because I'm bad in bed, not pulling my weight or whatever other shit those posters could throw. Nice.
Then there were the smug, almost mono-syllabic replies, 'yes it is cheating'. Well aren't you brilliant and profound.
But some posters did actually engage with the question, either agreeing or disagreeing, and it is those replies I'll address.
Marriage/cohabitation is by definition a sexual relationship. There was a poster who proposed several other elements of marriage, which might all be true, but to suggest it isn't at its core a sexual relationship is odd.
Perhaps a good analogy would be the definition of woman. For many people 'woman' means strong, empowered, maternal, resourceful, and many other things. But if you had to give a one sentence definition, it would be 'adult human female'.
Ditto for marriage/cohabitation. While it might mean shared goals, legal rights, combined responsibilities etc, the one sentence definition of cohabitation would have to be 'an exclusive sexual relationship', and for marriage it would be 'a (legally) formalised exclusive sexual relationship'.
All other aspects are certainly nice, and enhance the relationship, but at its core marriage/cohabitation is a sexual relationship.
When two people enter into such a relationship, there is an promise, either explicit or implicit, to have an exclusive sexual relationship. I say implicit because there are no vows in cohabitation, and even in marriage, most marriages don't involve the terminology 'forsaking all others'. That's a very specific Western/Christian phrase.
My argument is that when one party refuses to engage sexually, they have reneged on their promise. At the very least this should preclude them from having the right to moral outrage of the other partner reneges on their deal too.
If A never wants to have sex, how can they feel betrayed if B had sex with someone else? What exactly has been betrayed?
In general, the hurt from finding out your partner cheated comes from the feeling that you're not good enough. It's the humiliation of knowing the other partner saw you as lesser, and sought pleasure elsewhere. But how does this compute when you've made a choice not to provide for the other's sexual needs? What exactly was the betrayal, you can't have me but don't you dare go to someone else?
The argument was often brought up that in such a case, the partner who doesn't want to remain sexless should break up before looking elsewhere. But hang on, even if there are no children or complicated finances involved, breaking up has a high emotional cost. How much more so for the one who initiates, as nobody likes conflict. Should one partner be able to force the other to have to initiate a break-up?
How much more so when there are children involved or complex finances. It would seem some posters believe the onus is on the 'willing' partner to either remain celibate or only see their kids every other weekend. Can this be morally right? After all they entered into a marriage/cohabitation in good faith and have been keeping 'their side of the bargain' so to speak. So why is the moral choice to get screwed over, rather than 'cheating'?
It's been suggested that if the 'willing' partner finds sex elsewhere, they are just a coward who wants to have their cake and eat it. But surely the same could be said for the partner who stops having sex. Aren't they the same coward who wants the benefits and stability of the relationship, despite not keeping to the basic definition of marriage?
Now I'm not suggesting that if a woman isn't going at it daily one week post partum, the husband has the right to cheat. That is a ridiculous strawman. But if the frequency - and to an extent quality - unilaterally declines, that is a different issue.
If one partner stops being in the mood ever, the onus should be on them to examine why that is and what they can do to fix the situation. They shouldn't need to wait for the other partner to come crawling and have a chat. Certainly if they wish to remain in the relationship and benefit from it. And if they don't do that, imo they've lost the moral high ground and can't complain or become indignant if the other partner finds it elsewhere.