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"So I assume that if a man wanted to stay married to a woman and never sleep with her none of the women here would think she had a right to get it elsewhere."
If the marriage vows included the typical fidelity parts, then no, she wouldn't have a right to "get it" elsewhere. She'd have every right to sit him down and begin re-negotiating the relationship, however. Opposite situation, he'd have the same right. Just looking elsewhere for sex is cowardly. If you can't talk to your spouse about something like that, you obviously need to divorce. And divorce, well, that's re-negotiating the relationship, yup.
It's hard to make a call on this without witnessing what's going on with these people. The LW doesn't include any examples of what he perceives as direct and explicit quid pro quo "I'll fuck you if you (whatever)" behavior. It's possible that his wife doesn't perceive the situation that way. There's definitely a problem, and the wife definitely is part of the problem, but that kind of forward thinking architecting the manipulation is often in my experience the product of the brain of the perceiver. It's a lot easier to manufacture that kind of strategy in the imagination after the fact than it is to create a cunning plan and carry it out over weeks/months/years. The wife may indeed perceive that the Celexa has taken away her power, or she may simply be responding in a natural way to having her vanity insulted. She's used to being desired. It's flattering to her. To no longer be desired (at least the way she's used to being desired) is probably insulting. People in general tend to want what they don't have, so now that the desire is no longer omnipresent, she may just miss it.
Either way, this needs to end. The LW is either someone who is paranoid and fearful and distrustful of his wife (or maybe everyone) and the wife would be better off without him, or the wife is a truly heinous creature and the LW would be better off without her. Or some combination of the two, but the point is: the LW perceives her as an adversary, and has perceived her that way for a very long time. They're enemy combatants, and that isn't going to change for the LW. They should disengage.