Our daughter was like this and I just allowed her to skip meals. I did try to have at least 1 healthy thing served that she liked at each meal.. She liked raw carrots, celery and cucumbers.. so that was always available.
We did not make a big deal out of meals.. ever.
I also tried to give her choices.
Should we have spaghetti or pork chops for dinner? Should be have green beans or peas?
Sometimes she said none of them, so I would say ok, mom gets to pick!.. I still served her very small portions and if she tried it great. We would tell her, Thank you for trying. If she did not try it, we did not say a word.
Here is what blew me away. One day I needed to drop off something at daycare. I peeked in the window on the door and she was eating lima beans! and BEETS! I later asked the teacher if our daughter was a good eater.. she said yes, all of the kids are good eaters! I mentioned the lima beans and beets and she admitted the kids ate food she would not even eat.. I guess there was powers with all of the kids being served the same thing and watching each other eat..
I did discover our daughter did not like casseroles of any kind. So I would keep the items separate for her, but still serve her a small portion.
She is an adult and still does not care for casseroles, but does like sauces she can pour the portion herself.
She is the cook in the family and loves discovering new foods and preparing them.. We like to tease her a little about all of the raw veggies she ate. Like a rabbit..