A wise man-- L. Neil Smith, to be specific-- once wrote: "Many of life's tragedies -- and comedies -- arise from a misconception women suffer under that sex is optional."
It depends on what you mean by "optional". I wouldn't say anyone owes anyone else sex, but if you are under the impression that you are in a relationship, but you are suffocating your partner with a lack of sex, the "relationship" probably mostly exists in your mind. Sex might be optional for you, but if it isn't for him (and it's almost certainly not) there are going to be consequences if you don't face it and change something. Yes, it is your responsibility to change if you don't want him to find relief elsewhere. Sorry to inform you of this fact. You have the right of first refusal; don't be surprised or complain over what happens when you exercise it.
And whining or screaming about "cheating" isn't going to fix anything.
If you cut him off and he finds someone else, he isn't "cheating". You already are. If you have a guy who agreed to enter into a monogamous relationship with you, and you have cut off the sex, you are cheating on him just as surely as if you were doing the pool boy on the side. Yes, really. He agreed to monogamy-- sex with one person, not NONogamy-- sex with zero people. Zero is not one, and that's no longer monogamy, even if you wish it meant that as well.
"Cheating" isn't only about one person having sex with someone other than the one person they agreed to be monogamous with. It is also about one person deciding unilaterally to end the sexual part of the relationship while pretending the relationship goes on-- including continuing to fall back on all the jealousy and whatnot that goes with the average sexual relationship. He may be OK with that, or he may not want to face your wrath by admitting to your face you are strangling him, but he is under no obligation to put up with this situation unless the current arrangement was by mutual consent. If it wasn't, he can't "cheat" no matter what he does at this point. You have already broken the deal.
You might complain that he didn't warn you first. Yet, he probably did; you just didn't listen or didn't take him seriously. You might have scoffed or tried to make yourself out to be the victim. How often must he express his pain to you, only to be ignored, insulted, or threatened? Once a week? A few times per year? Every five years or so? How often would be enough to get you to listen, and not use his vulnerability as a justification to hurt him even more?
Not only are you a cheater, you are also an abuser. Withholding sex, and demanding he not find it elsewhere, is emotional and physical abuse. It causes emotional agony and physical pain. If you hold him to your toxic arrangement by threatening him with a devastating divorce, where you "take half his stuff" and force him to support the kids whether you ever allow him to see them again or not, I consider you evil. Others may cut you more slack.
If any of this upsets you, you may need to take a close look at yourself and see if you are guilty. In fact, if you are offended you may be the person who needs to hear this most of all.
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