I think people are missing the point. It's not that meat-eaters cannot survive one meal without meat. It's not that people cannot go to one dinner without alcohol... they can. But a wedding is a celebration and a party, and be honest, for most people a party without meat and/or alcohol is... well... disappointing. I can eat vegetarian food, but I am always left feeling "unfulfilled" and hungry in the end, not because of not having enough food available, but because with a veggie dish i never really feel like eating too much of it, for me it feels like it is lacking something (meat?). Of course I would never tell the bride and groom this, but they need to acept this is exactly how many of the guests are going to feel. And plenty will go home and feel the need to have another dinner.
The examples given of how carnivores often have a bowl of cereal or beans of toast are also beyond the point, as most people do not expect these dishes at a wedding.
I think this puts it very well indeed. It's your wedding and entirely your decision, but it's also a celebration where people expect things to be special. It's all because of you but it's not exclusively all about you - it's an event for all of your friends and family.
We don't drink alcohol - just don't see the point of it, but we ensured there was wine and champagne available, as we know that most people enjoy it, consider it as very important and would hope/expect it at a wedding. Yes, they could have managed a day without alcohol, but a wedding isn't about managing - it's a time of pushing the boat out; and, as well as the people getting married, we were also the hosts.
You might as well say why do you have to wear an amazing dress and get your hair and makeup all planned and done perfectly - the getting married is the actual part of the wedding and you have plenty of occasions when you can wear fancy clothes and get your hair done beautifully - surely you could go just one day in your jeans, as you freely do this out of choice most evenings and weekends anyway?
You could be very focused on health and have a standing desk at work and therefore consider it just normal, so you might decide to have a 'healthy' wedding and do away with chairs for all except the disabled and very elderly. Surely you can just stand for a few hours, can't you? Yes, they can - but most would far prefer not to.
For most meat eaters, they don't need meat all the time, but it is a standard part of a really special meal. A proper celebratory meal without meat for them would probably be the equivalent of a bowl of macaroni cheese for you - perfectly adequate, but nothing special or befitting of an important occasion. You wouldn't eat meat 'just for one day' at your own or anybody else's wedding, so don't expect them to be thrilled at not being able to eat meat for one very special meal.
I don't think you'll ever find any common ground as, whereas vegetarians tend to see meat as a cruel, wholly unnecessary addition/alternative to a perfectly amazing meal, most meat eaters will see a meal without it as not a proper full meal. Yes, a meal that will satisfy one's basic hunger, but not a full main meal. People, whether vegan or omnivore, will have a bowl of cornflakes for the functional energy and sustenance rather than as any kind of special celebration or something to get excited about.
So yes, absolutely, have things exactly as you want them - as long as you realise that some people will be disappointed and don't expect them to be as thrilled about things as you are. For them, it will be a negative part of what is, overall, doubtless an otherwise very enjoyable day.