Of course they are inforcing being a vegetarian as they are not giving the option of eating meat and other animal products. At a young age children should have the opportunity to experience a variety of different tastes and textures(unless there is an allergy)
I don't feed my daughter meat, as I don't eat it or cook it myself, and neither does DH. We both used to be vegetarian but have eaten fish since before dd was born, so she eats fish too. I don't regard meat as being particularly healthy, so why would I rush out and buy it for dd?
I have always told her that she is free to eat meat outside the home ie in school or at friends' houses if she so chooses. I don't have strong feelings about it and wouldn't really mind if she chose to eat meat when she is older or not. So far, however, she prefers to stay "pescatarian".
Am I inflicting this diet on her? To an extent, yes, but it is her choice too. And we all inflict our own dietary choices on our children, don't we? I don't feed dd beetroot, for example, because I can't stand the sight of it. I am guessing that you probably don't feed your child dog meat, because you wouldn't eat it yourself. That isn't denying your child the opportunity to try something different, it's just common sense.
If I were still a vegetarian, I would feed vegetarian food to my child. If I was a meat-eater, I would feed her meat. If I were a vegan, I'd feed her vegan food. It's very simple. BTW, DH was brought up as a vegetarian and is the only one of his siblings who eats fish, let alone meat. So veggie kids don't always rebel when they are older. And although my eating habits are different from those of my carnivorous parents, I don't regard that as a rebellion either. 
OP, well done for admitting that you were BU, but I do find it very weird that you commented on such a non-issue on FB. 