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I suspect that there is a lot more to this story, and I think we'd need to hear the wife's perspective too before passing any judgment on the topic. It's not uncommon for women to lose interest in sex when the kids are young, for a lot of reasons. It's also not uncommon for women to lose interest in sex if they are depressed, or if the sexual dynamic has changed (like if they start to feel pressured constantly by their partner), or if they change their birth control pills, or any number of other reasons. It's also possible that the wife has issues from the past (like sexual abuse or sexual assault) that might be influencing the way she views and experiences sexual relationships. But we don't know any of these things - in fact, we don't really know anything about the wife AT ALL. All we know is how her husband is perceiving the situation - as her being manipulative and withholding sex. But in the letter, he doesn't make any effort to explore WHY their sex life is the way it is, other than casting himself as the victim and her as the bad guy. I'm not buying it.
The fact that she wants him to get his sex drive back tells me that something has changed in the relationship, she has noticed it, and it probably makes her feel insecure. She's used to him wanting her, and now he doesn't. She wants him to want her again. There's nothing nefarious about that. Maybe he's not showing her that he wants her in any other way, and that is something they need to examine as a couple. How else can you be affectionate and foster emotional intimacy without having sex? If you can figure that out, the sexual stuff might eventually fall into place. It can be a real turn off for women when they feel like the only positive attention they get from a partner is sexual. So this experience with the anti-depressants might free the LW and his wife up to figure that out, and to foster non-sexual intimacy in their relationship.
I'm also concerned that this couple apparently had kids and yet not once in the letter does the LW mention this as part of his stay-or-go thought process. I'm not saying you should always stay together for the kids, but their well being should at least occur to both parties.