Good grief that's a reiteration of my past life and has brought back so many memories as I know exactly what you mean. Lovely loving husband and a terrific person all round, but ... incapable of spontaneous physical affection or desire So you sit on the sofa and cuddle closer and he just shits away, ask why and he says "I thought you'd be more comfortable". Hold his hand and after twenty seconds he lets go, "my hands all hot and nasty" he excuses. You hug him, and it's like he's hugging his mother. You kiss him and he says "I haven't brushed my teeth recently - you don't want to kiss me". Sex? Hahaha. No chance. Dwindling to nothing in the last ten years together. Separate rooms for the last five years (much better all round).
In my case, absolutely nothing worked. And I tried everything. Marriage counselling. Endless talking, arguing, begging, threats to leave, to have an affair, weight loss, made more of an effort. Nada. Zilch. He'd say he'd change - and never did for more than a few days. But such a great father! So thoughtful and supportive of me, too, in every way but physically.
I had a miserable lonely time of it. Self esteem plunged, particularly after age 40. So I had affairs with single men - and almost wrecked my family life that way. Chaos. Torn in two emotionally. Guilt. Shame. Loss of focus on my young DC.
It was a terrible decision and something I now feel horrified and ashamed about. I actually thought my ex knew and had agreed to this - as I'd said if he didn't want me I'd find someone who did. But I was wrong and he was jealous ... cue mutual remorse and sorrow and again, we agreed to restart a physical relationship. So we did, for a week...
And throughout, he said he loved sex with me... so why not do it then!! I got so angry and confused and miserable - I tried to leave, could not face sharing 50% life with my kids ir taking him from them - he loved and cared for them throughout every single bit as much as i did, was as much their parent as i was.
So finally I got a grip, refocused on family life and work. And had no sex or even a hand hold or a kiss for 10 years. It still makes me very very sad.
I left when our DC were young adults.
And he and I are now the absolute best of friends. I can love him so much more now that we don't live together and I'm not expecting or hoping or feeling ashamed for wanting him to just hold me close. And he's not feeling guilty and ashamed because he's letting me down.
In the calmness and loving relationship we have had for the last decade, he has never ever looked at another woman. Nor me a man (thank god for the menopause). We still don't have sex or hold hands for more than a few minutes. Or sit close. But he hugs me now.
He says, now, that he just doesn't think about sex. Doesn't masturbate. That the idea of sex just repels him. Swears he's not gay (and I believe him). I think a man feeling this way today would describe himself as a-sexual. I think he simply does not feel desire or pleasure in touching others. Now though, his hugs and warmer and longer and he says far more often that he loves me and compliments me.
It was a terrible environment for our DC in many ways. Tensions under the surface, a sad, mad and bad mother. A father aware and ashamed that he was not making their mum happy.
But also and at the same time, it was far from all bad. We parented well together. We had fun as a family. The DC say now that we were good parents, that me and their dad were funny together, that there was a lot of humour and sense of belonging. And that they did notice we never held hands etc like other kids' parents. They say they are glad we stayed together as a couple - but can also see how much happier we are living alone now. He like your DH is introvert and lives very much in his own world.
OP, my heart goes out to you. We don't make a mistake with these men. They are good, loving, special and loyal men. They just do not think about touching their partner, ever! They don't lie or drink or gamble or betray, they don't call us names or hit us, or withhold money or blame us for working. In many ways, they are perfect family men. A great many women would swap their useless husband who paws at them in the kitchen, is addicted to porn and wants sex every night, and ogles every woman they see, for your life.
If you stay, then this is how your life will be. Only you can know how important physical touch from someone who you love and you loves you, is to you. Casual sex lacks love. Loving women friends give affection in buckets, but without desire. Small children adore you ... but from about 12, they hate you.
So my heart goes out to you. Think deeply, love yourself, and know that life is just one long period of change. What you cannot bear today, may bring you peace and calm tomorrow