S.R.
I'm an adult. I eat what I want. No one forces me to eat anything. If I want to eat grilled cheese, cereal, and chicken patties the rest of my life, I can. But I have to make them myself, or go hungry if they are unavailable.
The age of the kid definitely makes a difference here. Can the guy get his own cereal? Then let him.
No matter the age, the kid needs to learn the appropriate way to refuse foods he doesn't like/want. Gagging is not cool. I'd say work on the expectations around how to say "no thanks" to something one doesn't like, rather than how to make oneself EAT something one doesn't like. Because in reality, we humans do not eat things that are not appetizing to us.
My input is: keep offering, keep offering, keep offering, But accept the refusal. Have the short list of back-ups they are allowed to grab/prepare (on their own). And then give the kid a multivitamin at the end of the day.