This upset her to the point of tears. Saying I only want her for sex etc etc. I just want sex. It's not the only thing I want. I like plenty of other stuff about her she just won't listen.

Alright for some reason or another a lot of people feel like if you value sex in a relationship then all of a sudden that's all you care about.

Now obviously they care about stuff other than sex, but as demonstrated in your OP she does care about sex on some level. So the trick is to get them to see that sex is important at least on some level so that without it, it can cause damage to a relationship, but that you're not gonna dump your partner if they should get in a accident and can't or something like that.

You accomplish this by showing them that they care about sex (because lets face it almost literally everyone does). To do this you get them talking. For example, "Why would you (or someone) want to wait until marriage to have sex?" Or "Would you be fine with me having sex with other people if you won't until we're married?" Now obviously this is cheating which they will not be okay with. But why aren't they okay with it? Blah blah blah at some point in these hypotheticals what you're looking for is "sex is something special". Because why wait if it's not "special", or why does it matter if I have sex with other people if it's not special.

That's the goal, it's something special. So now why is it special? The obvious is the obvious here, but you could have sex with anyone at anytime if it was just to feel good. So why is it special? Well you're gonna get answers in the area of intimacy or bonding between partners etc etc.

Then you close for your situation. You're surprised I would be unhappy without the intimacy and bonding (w/e their response was) for 3+ years?