See I find this very interesting. In my house one parent (me) is a meat eater and the other (DH) was a veggie. DH wanted to be a vegetarian from 9 but wasn’t allowed to be until he was 16. There were cost/time/availability issues in his family and the country he lived in (lots of children, only one parent home most of the time, little veggie convenience food available) but he still resented not having control over his diet so he has approached his children’s diet much more from the angle of wanting to give his children choice and listen to what they want rather than imposing his choice on them.
We’ve deliberately gone the other way and given our children a great variety of things to eat but also given them freedom to exclude and include as they wish. As a result my eldest is pretty much veggie now whilst the two younger ones are omnivores. We eat a lot of veggie food anyway and can make things non-veggie with small adjustments that don’t budget bust so it works for us.
I know plenty of families where vegetarianism is a decision of both parent and child and they very happily live that lifestyle. But I do agree with the OP that in some circumstances there becomes an unacceptable level of control where a parent is forcing their child to live by values they don’t share.
I think most of the sensible vegetarian parents I know accept that even if they are brought up entirely vegetarian, by the time they hit their teens there are going to be occasions outside the home where they may eat a few chicken wings or a burger off a barbecue and they realise this is a normal part of growing up and forming your own values rather than just being a little identikit of your parents. Frequently those children try then leave alone.
The foolish ones continue trying to dictate their teenagers lives in minutae even when they’re not with them, and that seems to be the best way of sending them headlong into an adult life stuffed with Big Macs, KFC family buckets and meat feast pizzas.
Although I respect the right of parents to choose diets that suit their families, I think trying to impose it on a child who is actively saying it’s not what they want is foolish and futile.
I have to say, having suffered from anaemia myself I would be saying to the mother in the OP’s case that she really needed to get it together and sort out his died so he was getting the right nutrients, and if she couldn’t manage it from veggie food she’d need to start considering whether a sick, tired unhappy child was worth it. Did she think her child would look back and agree that feeling so awful was worth it for someone else’s principles? I felt so awful when I had anaemia I never would haven forgiven someone who prevented me from having something that would make me feel better without that disgusting brown medicine.