I do, however, still eat meat. When I order a veggie burger and the waiter brings a beef burger instead. When someone doesn’t know I’m vegetarian and has already prepared and served me meat. When meat is left on the table and will go to waste if I don’t eat it. All of these are situations in which I’ll eat meat — and enjoy it!

Then you DON'T care about animals suffering. If you had cared, you'd send it back.

1. It's not what you ordered.
2. It's the message.

People shouldn't be forced to eat something they don't want, if you really didn't want to eat meat, then you don't have to, but in this case, eating meat doesn't seem to bother you.
If you think it's alright to eat meat because the animal is already dead, then why do you bother becoming a vegetarian? The supermarket has a bunch of meat that's been dead, what stops you from eating that?

The idea is if enough people stop, there is a lower demand and less and less animals will be killed. If that can't be achieved, it's knowing you did your part in trying to be moral towards the animals, much better than what others do.

This is because the reason I don’t eat meat is that I don’t like to kill animals or create suffering. If I send back the burger, deny the meat that has been served to me, or let the leftovers go to waste, I am in effect creating more suffering. I or someone else has to prepare other food, resources are spent to prepare it, and the meat that the animal has literally died to produce goes to waste.

The owners of the store will note down that there had been a burger wasted because it was sent to vegetarian. He will notice the demand for veggie burgers and increase stock on those instead of beef burgers.

You are not creating more suffering by denying the burger, you are pulling a really long string that will have an effect on the cycle.

You can't say you won first place if you came in 3rd, but claimed that if you had beaten 2 more people, you'd be first, so you technically won.

You didn't win. You're not a vegetarian.