I couldn’t decide where to put this reply but thought this was as good a place as any, please move if needed!
Hi @anon8189768, thought I’d write a response to this one and I hope it doesn’t come across negatively, it certainly isn’t meant that way. I can see this from your wife’s point of view. If cuddling usually leads to sex and she’s not in the mood for sex then I can see why she would avoid cuddling.
If I’m not in the mood for sex, I will try to get in the mood if my OH wants to have sex but it generally results in either rubbish sex (for me) or feeling grumpy or frustrated afterwards. If I’m not in the mood at all then I certainly don’t like it if my OH tries to touch my boobs, it just doesn’t feel nice, it’s similar to if he tries to touch me down below when I’m not in the mood, it feels uncomfortable and makes me irritable usually resulting in me pushing him away or getting snappy (or both!). It doesn’t happen often since I have the higher sex drive but it does happen occassionally.
Might it be worth a chat with her and agree to definitely not have sex but still enjoy a cuddle? This way you can show her that you can give cuddles without expecting sex. It might be a bit frustrating for you I know! Or you could tell her that you will let her initiate sex when you’re cuddling instead of you?
As for the fact that you think the ratio of cuddles turning into sex is lower than what she says might be because the times that stick in her head are the ones that have resulted in the strongest emotions. For example I’m always grumbling about the number of times my OH would rather sleep than have sex and the fact that I don’t do this to him. I probably do, I just don’t remember it because it wasn’t significant to me whereas being turned down when really horny and frustrated definitely sticks in my head! I still don’t think I do it as often as him but there we go 
Finally, I’m sure she doesn’t think that having sex with you is bad, she just isn’t in the mood. From a female point of view, arousal is very much in the mind - if I am not mentally in the right place, it is very unlikely that my OH would have any hope of getting me aroused regardless of his skills in the bedroom! It doesn’t mean that I don’t like the way he touches my boobs for example, it just feels very different if I am in the mood compared to when I’m not. Feels amazing when I’m in the mood, irritating and intrusive when I’m not. Don’t let it dent your pride / confidence 
Sorry if that’s a long rambling post and it isn’t meant as a critsism at all.