I am seeing that some people are missing the point I was trying to make, and others completely understand it. The moral debate is interesting however, I didn't expect so many responses!
@ButWhatAboutTheBees that's interesting logic. So things from bones aren't vegetarian, but things from an organ are?
Vegetarians don't eat anything from the animal, that you have to kill the animal to obtain.
Vegans don't eat any animal-produced products at all. So yes, including honey, milk, eggs etc.
@Snooglequack yes the calves are-but vegetarians generally still consume other animal products. Male calves are a bi-product and are killed as a RESULT of the dairy industry but not FOR the dairy industry, which is the distinguishing difference-I am talking factually, not in terms of morals here!
@Caerulea I did think the vegetarian options looked very drab and boring myself, but that could be a matter of taste-some people on this thread have said they look good.
The majority of vegetarians eat cheese, eggs and milk. That's what distinguishes them from vegans. The point is some cheese isn't vegetarian because of rennet (& sometimes other ingredients).
If a meal contains ingredients from a calf's stomach, it isn't vegetarian. Other types of cheese, yes.
I've never known a vegetarian who would deliberately eat parmesan-it usually contains animal rennet-although yes some alternatives are available. I have emailed them to ask anyway.
That customer sounds insufferable! I wouldn't go to a restaurant with a particular meal in mind that I wanted, if I knew that they didn't sell it, that's just odd. Like going to McDonalds and asking for fish and chips.
@Dibbydoos that's awful that pizza hut did that! Was it rennet that made it non-vegetarian?
@KirstenBlest as I said about the options for vegetarians, they don't look great! I've never heard of a 'sweet potato burger' before actually! But it sounds like an awful texture. Like offering someone a mashed potato sandwich!
Good point about the pesto-to be fair, there are a lot of vegetarian pestos about now so I didn't think that worth mentioning as much as parmesan which isn't a vegetarian cheese.
@Barleysugar86 maybe, or maybe she doesn't know?
I think some foodies would object to a parmesan alternative being the default option rather than real parmesan.
@squashedalmondcroissant that's absolutely awful-I'd understand if you said it was 20 years ago or something but surely it'd be better to just do a pizza without cheese? Most pizza doughs don't contain anything non-vegan and if they usually do, surely the restaurant can make/obtain some that doesn't!
You sound like you were a 'proper' chef (by which I don't mean, qualified/experienced etc. but who embraced what the job actually is!). I know a chef who is scornful of anyone with dietary requirements.
There's a 'proper chef' at a restaurant local to me who, as you've described, really likes it when someone with a vegan/gf/whatever attends as it gives him a new challenge.
@skyfalldown you're a pescetarian.
I take people's points about the vegetarians being perfectly able to avoid those dishes/this restaurant but that isn't the point I was making. They shouldn't put something that isn't vegetarian into a dish that they then state is vegetarian. If they don't know that, they should IMO.
@TheLazyToad cauliflower steaks are an insult IMO-and often almost as expensive as a meat dish.
@TheHateIsNotGood yes, it can be made vegan on request, I read that. However my issue wasn't that it wasn't vegan, rather it was that is labelled as vegetarian when it isn't. Many vegetarians don't want no cheese.
@Chickenuggetsticks vegetarians do eat cheese-but not ones that have animal rennet in them.
@Floorbard a lot don't. A lot of vegetarians like cheese, cream, eggs-they often wouldn't want a vegan option.
@Demonhunter the moral argument is valid but a different matter altogether
@mathanxiety I don't think anyone would go as far as to say moral stretch to bacteria!
@TriesNotToBeCynical that, again is exactly what I meant~!
@Goldiefinch yes! I've seen a lot of that sort of thing unfortunately. Pizza without cheese-same price as one with. Basic tomato pasta sauce no meat, same price as if it had meat. Strawberries and cream without the cream- same price.
@Isittimeformynapyet I almost sat and listed them all 
mine was an oversight to be fair, rather than me not knowing it was incorrect
@HollyKnight leather is not a by-product.
I do tend to agree on using all parts of an animal rather than killing something and wasting much of its body, however by definition vegetarians do not eat a part of an animal.
I am of the stance that someone whose living it is to know about food, should know about food.
@SapphireSeptember I am going to point that out to them-if it isn't 'real' crab then they need to label accordingly.
@Castle0 as @Mothership4two says, I am not sure why that's relevant? Nothing to do with my question.
@Anyotherdude my point is, I feel a chef should know these things. It's literally their job.
The treatment of calves has been mentioned to me many times as to why people turn vegan from vegetarian. There's a saying 'Every glass of milk contains a slice of veal'.
@kkneat which chain is that please?
@IbizaToTheNorfolkBroads which is that? Thank you for the recommendation!
@RubyOrca What I might choose to eat was not related my query. my AIBU was that I expect chefs to know about food and ingredients.
'Get this angry' -I am not the least bit angry.
I wouldn't call a vegetarian someone with a very restricted diet either. More so now while eating out, according to a lot of vegetarians who are not happy that most vegetarian options now are also vegan.
No, I don't know that. Because they labelled it with a 'V' and it also includes parmesan-unclear.
@Bellaboo01 la does it say there's an alternative cheese that's veggie friendly?
@DuesToTheDirt I've known it since I was a child-I understand why many wouldn't question it, but a chef should?
@WoosMama13 I may have come to agree, then I saw the other mistakes on he menu (some pointed out on this thread).