You state that he lost a lot weight and hit the gym. Is it correct to assume that during that period he also cut back on the drinking?
If so, he was doing at least one key thing that he knows is important to you and important to the health of the marriage. And when he asks, you still say no to sex.
This fits into his narrative of the marriage as you as the sexual refuser, and probably to his view of you as the endlessly refusing wife being a big source of both the marital strife and part of the reason he drinks.
So of course now that he's tried self improvement and focusing on bettering himself, and told you how important it was to him, and you still refused sex, he's very, very angry.
If less booze was part of his health and fitness push, then he tried making a big positive step and meeting one of your key needs, and tried bluntly communicating his needs, and you still said no. In his mind you're still just not willing to do what it takes for the marriage, so of course he's done.
There is another way to look at this....I do see what you are saying MartinBeck. Could it be that the relationship in the beginning was full of sexual activity and perhaps as young people maybe their relationship was sexually based as often times is the case with young couples. Children and work come along and OP and husband's hormones settle into this state of where they both were before they met, with his being 10x greater than hers which is biologically what is predictable. Husband still wants the sex they experienced before marriage or as newlyweds but OP would like a bit more concentration on family and their relationship beyond sex which again I think is common for both parties. Arguments may have even occurred on this very subject. OP is telling her husband that she needs ______ (maybe his help with the kids or around the house), she feels overwhelmed with the duties as mom trying to balance a career and simply put sex is not #1 on her priority list. I think for a majority of women this is a no-brainer. I would be willing to guess that OP pleased her husband many many times when she was timed, overwhelmed or sick to keep him happy which is also common for women.
Life in the military settles into OP's husband boozing it up with his buddies which I personally have witnessed time and again with the military men especially (part of a military family myself for 27 years) and OP does not like the ugly behavior she sees and she complains about his drinking, maybe she tries to limit it, maybe she walks away but she still doesn't like it. They already have distance from years of other issues which happens in marriage. OP's husband is unwilling to talk about the problems so there is no resolve and OP is not happy because of the years of unresolved issues. Her husband on the other hand is living life like there is no issues because he really never took her serious in the first place or did not see her complaints as his. Communication has broke down and the marriage is slowly deteriorating. he wants sex, she wants the husband she once loved back. The man that used to touch her without it being sexual....hugs and hand holding, and being told she was loved. She wants her husband to be an active father and take responsibility with with rather than being a passive, almost non-existent role in their lives.
He finally realizes he had better change something or she is going to walk. Rather than having a talk with her and telling her, "I know I have let myself go.....I have been drinking too much, I have been lazy and I can see why you have not been attracted to me. I would really like to put on marriage back on track. What can we do as a couple to make this work?" he opted to go to the gym which she might have been thankful for but wondering at the same time what the heck his sudden interest in the gym is all about and perhaps even suspicious that he had ulterior motives (like women seeking). Maybe he did try to cut back on the booze but in all the years together she has seen it before and she knows it won't last she she is just kind of coasting along kind of watching to see what is going to happen with all this. Then he pops out with the statement about losing weight and wants sex. Of course she is going to be befrazzled. These thoughts were not in her head. There were no issues that were resolved in the process.
A wife that is hurt does not just start sleeping in the spare room, nor does she just stop having sex with her husband for no reason. There was trouble in the marriage before these things ever happened. She was unheard, what she tried to do to accept, forgive, fix, please, or resolve the issues were met with deaf ears. She becomes stuck between a rock and a hard place emotionally and she feels like she wants to keep the family together but her needs are not being met by her husband. She is questioning whether she wants to stay, she realizes the man she once knew is no longer the man she is married to. She has spent so much of her time and energy in raising her children and meeting everyone else's needs that she doesn't even know who she is anymore, and more than likely something that had been expressed to her husband.
OP's brain is still tracking on sex and what he needs to fulfill his sexual desires, priority #1 in his life besides keeping a job to provide a roof over the family. OP is disgusted and feels all he wants of her is sex. She can't give to him anymore because that is all she feels she is to him anymore and maybe as she starts reflecting she feels that maybe that's all she ever was to him. Once a wife feels this I do not think there is any way to go back, especially if there has been any kind of infidelity, porn addiction and husband seeking the attention of other women. She will see that focus and separate herself emotionally from him to save herself. She might not even real what she is going thru. She just knows she can't be with him.
As far the drinking....no one was making OP's husband drink. He made his choices. It is his responsibility to find his way out of his own addiction.