The only rational explanation that I can think of is that your girlfriend does not want you to wash wet towels because she is a wet towel.
At least you guys always know where your towel is. That’s the first step to becoming a hoopy frood.
A 6 dm x 7 dm towel by any chance?
Again, I have to ask: “Why?” It might be a good idea to use a little less soap in that instance, but most dishwasher detergents have anti-sudsing agents in them, so even that doesn’t really pose a problem. . .
In fact, I’d think that drying increases the chance that the hair/skin cells/food have a chance to bind to the cloth fibres. If every stain known to mankind comes out easier if you wash it before it dries, how can it be true that washing them while they are wet is a bad thing?
I think the confusion here is with some idiot who thought they could put the used towels into the dryer to dry them. My idiot ex used to do that ans it made me crazy. He would even do it with sandy towels that had lain (laid?) on the beach all day. Then I would have to spend 10 minutes with Windex and paper towels getting the inside of the dryer clean again so that I could use it on clean clothes.
Grump, gripe, grumble, growl . . .
Unbalance the washing machine?
Nonsense. You should be distributing the material in the washing machine equally around the tub regardless of if they’re wet or not. And if you don’t, I’ve found the natural agitation of the washer will distribute things around eventually. The big issue is the spin cycle following draining (most washers have two). Now, I’m sure we’ve all at some point had to rush over to the washer because too many items had situated themselves on one side, and our washers began to dance. This was especially true of older washers that didn’t have the “floating” tubs. Anyway, by this point, the clothes have been washing and agitation in a tub full of water for over 10 minutes. Someone explain to me why the hell the towels being wet or dry going in would be an issue here?
ALL washers I’ve encountered on this planet will have the clothes soaking wet before it begins to actually clean/agitate as filling is the first step. Depending on how your washer is designed, you’ll either insert clothes before it fills, after, or you’re given a choice. Our current washer requires that you place the clothes in first, and it automatically fills with the appropriate about of water. Our old washer was manual, and you chose if it was going to be a Small, Medium, or Large load. Either way, these suckers fill and then begin to do the deed.
Those of you with fancy front load washers have even less to worry about.
I cannot even believe this is a debate, and it reminds me all too well of asinine arguments I used to have with my ex.
Try this, it really confounds my GF. Dry yourself off with a wrung out wash cloth first (like shammying your car) and then finish drying off with the towel. Towel never gets overly wet, just a little damp. She has yet to figure out why my towel is always dry/damp and ready for use while hers is still soaking wet throughout the day!
It is certainly not a good idea to leave wet towels balled up at the bottom of a hamper to stay wet for days. That’s doesn’t mean you have to let the towels dry before washing. Although it might be a rare event for the machine to be loaded and ready to go when someone comes out of the shower, it is not such a rare event for the towels used a few hours ago to still be damp/wet even though they are hung to dry. No reason not to throw them in the machine. I could be misunderstanding, but I think the OP is talking about washing those towels until they are completely dry. And that makes no sense.
By all means, you should let them dry first! 
When I began living with my gf, she was shocked by how I did my laundry. I put everything together in a single load and wash it in cold water. She separates whites, like colors, delicates, etc. Then she takes the “dry clean only” stuff to be dry cleaned.
Sure, I’ve destroyed a few things. But in the long run, those were items I should not have purchased.
Words of wisdom. I’m not allowed to do the laundry either since my method is two piles: lights and darks. Funny how I survived for 10 years on my own like that.
I’m barely allowed to use the dishwasher either, since you know, I actually put dirty (un-rinsed) dishes in it and sometimes even large items that take up valuable space. 
OP’s girlfriend was probably told as a kid not to put wet towels in the hamper and in kid logic that = don’t wash wet towels. That would explain why Mom didn’t get her logic either.
Not the dishwasher soap, just the water. A single soaked towel in a washer can shake a house like an earth-quake when the spin cycle starts. (I have been in two minor earth quakes; they were strong enough to make the news.)
Nice think cotton holds more water than you might realize. I don’t quite understand how one previously sopping wet towel can be heavier than others even after they have all agitated together for ten to twenty minutes, but it does happen.
Maybe she’s worried about overloading the machine. Wet towels take up much less volume than fluffy dry ones, so you might end up putting too much stuff in the machine.
No, I simply meant that you hang your towels up after using them so they can dry, instead of crunching them up. Yes, if they are damp, but I’m loading the machine, then they go in.
Yes, I vote for that as most likely: a misunderstanding when Mom told her what made sense and getting things mixed up. Reminds me of similar “family traditions/ Mom taught me that” stories
Shenanigans.
You loaded that side of the washer too high because the wet towel wasn’t fluffy like the clothes/towels you put in the rest of the basin. More fit on that side, thus the wonky load come spin cycle. You also overloaded the entire thing, or it would have evened itself out during agitation.
You do realize that a guy who owns some jeans and t-shirts and washes them all with the standard program of 40 C (or maybe even the cook program of 60 C) will not have the chance to ruin much, while a gal with blouses made of silk and thin, delicate cotton or other materials will quickly ruin them in the standard program? Or that getting a whole load tinted pinkish because there was one red item is much more a problem if each blouse costs 40 Euro, compared to a cotton T-Shirt of 10 Euros (or even a man’s shirt, where a package of 5 costs 30 Euros)?
Just because you didn’t see the difference in your stuff, doesn’t mean it was dumb of her to be more careful.
Wow, what a rationale. Does that mean you shouldn’t have bought nice clothes, only ratty stuff, or not expensive things, only cheap stuff? Or not stuff that needs to be dry-cleaned? Not everybody can wear only jeans and T-Shirt to work and some people like to have nice blouses and good blazers and so on, but the different materials and construction means you have to take better care of them.
I do partly agree on the last one - I have stopped buying stuff that can only be dry-cleaned, although I know that : I can wash by hand at home stuff that should be “dry-cleaned” with the right procedure and soap; and companies have started putting ridiculous temps. on the labels in the last year for fear of complaints. So a sport shirt says 30 C on the label, although it needs 60, because if some idiot uses 95 C and it shrinks, the company doesn’t want to be blamed. So some obvious false labels I ignore, using common sense about the fabrics and sewing method.
The ONLY time I separate my clothes is if I’ve just bought a new item that I think might bleed in the wash. The other 51 times a year, I wash everything together with no problems whatsoever.
Sure to all. Different strokes. I am self employed and am very lax in the wardrobe area. I have nice stuff, and spend some $$ on clothing. But I’m not going to take stuff to be dry cleaned, and although I’ll wash a brand new bright red shirt separately the first time, I get results I can live with by washing everything together.
As some comedian has said, “Dry Clean Only” can be translated to “This Item is Dirty”.