Why do airlines offer more varieties of special-request meals than they actually provide?

Another member already mentioned in his answer (now deleted), that adding those pre-selection options is very easy compared to actually catering them. I will try to elaborate on why this makes it actually desirable to offer those options in pre-selection.

It's more intuitive

Imagine you're booking your ticket online and come to the point where you have to select your meal option. The options that are presented to you include vegan but not vegetarian, as that's not served on the flight. If this is the first time you're booking a flight, you might not know yet that there will be no specialised meals for vegetarians. In this case you might start wondering why there is no vegetarian option. Maybe it's missing? Maybe you should call the hotline and ask them why there is no vegetarian option?

If it comes to that they already wasted your time and brain power and if you actually call their hotline because of that, it will also waste the time of the person answering your call. This waste of time could easily be circumvented by just offering all options, so everyone finds their option immediately.

This problem could also be solved by putting a note next to the selection that explained why some options are missing, but this would probably not be as effective, as it is terribly hard to get a computer user to actually read notes.

You also mentioned in the comments that you usually have to declare you dietary needs by calling the airline. In this case it might look like my argument doesn't apply since the customer doesn't have to select the option themself. However, the person answering the call still needs to make the selection and they will probably do it in a similar manner to what the customer would do when booking online.

People answering calls at companies are usually trained in some way, so the company could just train them to select vegan if someone says they're vegetarian. This would make the vegetarian options superfluous again, but you also have to consider the cost to train your employees about one more thing and while that probably doesn't add much to the overall training cost, it is probably still cheaper to skip this in training and just let the phone operators believe all the options actually matter.

I don't think this is the only motivation to offer these options, but from an IT perspective this definitely makes sense.

Because meals are prepared on what is essentially a factory line, they are not prepared individually as a restaurant meal is. Food prep people just dish up foods to create a handfull of menus which are loaded onto multiple flights. The more special meals you create, the more workstations you need.

I also believed that maybe some ME airlines may have multiple different vegetarian options, until I tried Qatar airways in February. They had like ten different options to choose from, but on the flight it seemed they did not have anything but "with meat" or vegan.

However, I personally know of two other reasons for your wide variety of choice:

Case 1: You can select your option for the (rare?) case that not enough vegan meals have been loaded, (maybe due to urgent rebookings?). In that case, the most lenient vegetarian will get essentially leftovers thrown together. No warm meal, which contained meat, instead, two or three each of the green salad with caesars dressing, yoghurts and cheesecakes taken from surplus meals with meat. To do this, they had to know who would eat dairy and who wouldn't. (Source: I was seated next to that poor(?) fella on a flight to Rome a few years ago.)

Case 2: There is more than just a meal on a long-distance flight. There are snacks, which may already have a vegetarian, non-vegan option. The choice on KLM once was "cheesecake" (on a side note, KLMs "cheesecake" is with Gouda, not curd) or Chicken Sandwich, with meat-eaters having choice, vegetarians being served "cheesecake" and only vegans receiving a very special treatment.

Consider that the yoghurt and cakes they serve might not actually be vegetarian - gelatin (could be in both), insect-derived red colorings (cake), potentially tallow/lard-derived emulsifiers (the E47x group of food additives... could be in both), natural flavourings of unknown origin, bone char derived sugar, casein from rennet-containing cheese are all ingredients that could be inacceptable to a person of which the only thing you know is that they ordered an ovo lacto vegetarian meal (to somebody insisting on 100% ovo lacto vegetarian diet, all of these would be unacceptable!).

Keeping an eye on what nationalities of passengers tend to fly along on your common routes could give good hints whether eg AVML style meals might be a common order and well available.

Another reason to offer all of those requests even when they'll all be fulfilled with a vegan meal is to track them.

If an airline only offers vegan and non-vegan then they have very little basis for actually offering anything in between in the future as there will be virtually no record that anyone wanted them.

If lacto-ovo vegetarianism became the next big fad among people who previously had no medical or religious dietary restriction, an airline could see a large uptick in those requests and order an actual meal that meets it, then subsequently promote that to capitalize on a growing group of people who are underserved by other airlines.

That's probably never happened (it's just one example of how that data may be used), but it's the best way to track the data for such a use (or for many other uses I haven't thought of).