I think posters who blithely say children are fussy because they have more choice now have never come across a fussy child, tbh.
my dd2 is a very faddy eater (and I never thoguht I'd say that - dd1 is ASD, has soe pretty serious food/drink issues, but the fussy/faddy one is dd2!)
she has never had a choice in what hse gets (I occasionally will ask her, and she does now get a choice of what she wants for lunch - well she gets to state her case, but she can't have jam sandwiches everyday!).
I cook one meal, for the dds. it is a gluten and dairy free meal. they can have fruit after (I am not interested in them going hungry), but there is generally no choice as to what the meal is.
dd2 can eat it, or not. she can have some banana afterwards, but nothing else.
she is really quite fussy. and picks and nibbles at everything.
doesn't like anything.
it gets quite tedious, but believe me, we do not pander to it.
agree with bubble - the sure fire way to get her to eat something is to have it on our plates and then she is interested in tryng it, but still will say "no thank you" if we offer her some for herself.
she'll grow out of it one day
(and it is no different at school - she is not fooled by peer pressure. she will often come home and say eg "I had ham, potatoes, peas and tomatoes today. I ate the ham and I tried a little bit of tomato")