Have you considered trying to cook them better? There is a vast difference in range and quality of how tasty veggies can be based on how you cook them.
For example people boil brussel sprouts and then wonder why they taste like crap. Those things needs some char on them and need some good roasting to bring out the flavor. Carrots have a ton of opportunity but also need some real heat to get a char going (try with some white miso on top).
Ah, yesssss…the ol’ Bread and Jam for Frances trick. Diabolical.
Any lightly steamed green veg can be rendered palatable by drizzling good olive oil over, a few dashes of Kosher salt, and a couple squeezes of fresh lemon juice. Doin’ it Greek-style.
As mentioned before, kids really do have a different sense of taste than adults. More sensitive. But it’s aroma and appearance too, especially as it relates to how it’s prepared.
When I was very young, I disliked most vegetables. I thought it was just the way it was. Turns out that my mother was just a horrible cook ( back then ), as I was to find out as my world expanded and exposure to other’s food preparation increased.
There are whole books and websites on sneaking vegetables into kids diets, but most pediatricians say don’t make a BFD out of it. *My friend had a ‘3-bites’ rule for her kids, before they could get desert, three bites of green beans, broccoli, carrots.) Most kids like fruit, you could give them slices of apple or canned peaches, for the sake of their bowels. Make a smoothie with some bland tasting vegetables, pulverized and disguised with the taste of banana or chocolate frozen yogurt,
Never force food on a child. You are setting them up for more problems with that approach.
They like meat? Put a small portion of veggies on the plate and cover it with meat. M SIL did tis with her picky kid, and the kid loves veggies covered with meat juice.
Try scrambled eggs with veggies and cheese.
Ditto this. Except for the mealtime torture part–there wasn’t any.
Whether I ate or didn’t eat something was NEVER an issue. My mother would make BLTs and I’d take out the lettuce. She’d make stuff cabbage, and I’d just eat the filling. Same with stuffed green peppers-- I’d just eat the filling. She never said anything, and it was NEVER an issue. Now I love all veggies and will eat any of them (except cilantro). This is not a battle worth fighting. IMHO.
Carry on.
Don’t make a big deal about it. Keep trying different vegetables and ways of preparing them.
Do they like potatoes? It’s hard for me to believe anyone doesn’t like potatoes but they get short shrift as vegetables when they are quite nutritious. How about tofu? It’s a sponge that you can make taste like anything.
Puree them up into yummy soups and sauces that cover the meat…think about beef stew or chicken stew with vegetable stock, blended carrots, onions, squash, etc. Pot pies. Make meatballs and meatloaf with veggie filler (oats, carrots, etc).
My kid refuses to eat any meat. I do the reverse to get her some meat protein, like pureed meat or fish to spread on her fresh strawberries. Gross to an adult, but heaven to a 1-year old.
I was a picky eater kid. My mom didn’t force me to eat food I didn’t want, but she didn’t make alternative food for me. If I didn’t want the veggies I didn’t have to eat them, but I didn’t have a second choice. I’m still alive and healthy at age 62. There are only a few vegetables that I really like, and I’d be happy to never eat another vegetable.
Your children might prefer them raw. Offer a plate of carrot sticks, celery sticks, broccoli florets, grape tomatoes, summer squash, grape tomatoes, sugar snap peas, etc. as snacks or with a meal. You can serve yogurt dip or hummus with them.
Try making “sludge.” Ad 1/2 of a can of water to a can of soup. Heat to boiling. Take off heat and add a four serving package of instant mashed potatoes. Serve and eat. Any flavor soup and potatoes work fine together.
My mother used to make it, and we all loved it. And my sister’s kids and grandkids and my borther’s kid love it.
Show them on youtube how they kill and carve up a cow ?
I mean how the cows are killed and carved up
My kid didn’t like meat besides tenders, nuggets and fish sticks, and didn’t like green veggies or really any vegetables. I never gave up offering veggies, trying new ways to serve them and made sure we modeled good eating habits. Her friends would see she avoided meat and called her a vegetarian like it was an insult and she felt insulted too!
Well, college vegan friends opened up her world to veggies and vegan options. The kid is a bone fide vegetarian now, loves all manner of veggies though not big on green salads. Squash, legumes, kale, chard, spinach, chickpeas, chia seeds she even loves brussels sprouts, ( I like em too but I don’t love them like she does now) Helps that the kid can cook, and likes to spice it up. Her soups are amazing and casseroles take the centerplace on our table when she visits.
Your kid may out grow here aversion or may not but she’ll survive. Ignore the chest thumping proud parents who kids eat everything and never pick over their food.
There’s a couple of different things that might work, or might be going on:
Turns out a lot of the stuff I didn’t like when I was a kid I was actually allergic to. Well, yeah, if eating something makes you ill odds are you aren’t going to like eating it. (Unfortunately, as time went by and my immune system decided to object to more and more stuff there is now a list of stuff I do in fact like but can’t eat any more unless I want to risk spending the night in the hospital.)
It’s the way it’s cooked (or not cooked). Kids don’t like raw vegees? Try steamed. Or a sauce over them. Kids don’t like cooked vegetables? Try them raw. (My late spouse used to like raw turnips, as just one example) Try different sauces.
You kid might be a “supertaster” of some sort. There are people to whom the entire cabbage family tastes horribly bitter. There are people (I’m one of them) to whom cilantro tastes like Pine Sol floor cleaner. You’re not going to convince such people to like that stuff that tastes like soap or worse. So try different vegetables from a very different family of plants.
The kid just doesn’t like vegetables. So try fruit. This can also work in reverse, as some people don’t like fruit.
I’d say keep trying, observe to make sure this isn’t a case of something making the kid feel like crap, and if all else fails apply vitamins. Kids can survive a less than perfect diet, it’s more important to not give them eating disorders. If they do have an eating disorder or intractable food/vitamin deficiency then seek actual professional help and not advice from random strangers on an internet message board.
Smack them with a Bible when they refuse? :dubious: 
(Ha, ha! Just kidding!) 
This is the first thing that crossed my mind as well. For the most part I would rather eat raw or lightly steamed veggies.
Serve your kids vegetables that have a pleasant texture. The tops of broccoli can feel weird. Mushy stuff like cooked zucchini will often be rejected because of the mouth feel (that’s why I don’t like it).
Consider serving raw veggies since they often have a better texture and more subtle taste. Raw zucchini, butternut squash, cauliflower, carrots and beets are good choices.
Roast vegetables like broccoli, brussel sprouts, and kale. Toss them with a little olive oil and salt and put them in the oven at 425 until they start to blacken and they taste great.
Make soups with spaghetti squash instead of pasta.
Serve smaller servings of the meat so they can’t fill up on it and will have to eat their veggies.
Put a party plate of raw vegetables out on the counter while you make dinner for the kids to snack on until dinner is ready.
Instead of regular potatoes, serve sweet potatoes.
Beat them with sticks.
Or-- feed them the food and what they eat they eat and what they don’t they don’t. My kids went through about a million phases growing up. One didn’t like anything colored green when they were 6. One decided they wanted pancakes, waffles and French toast un-adorned (not even butter!) for all of his elementary school years. They both didn’t like steak for a very long time (too chewy, they said). They would hate peas one day and love them the next. Couldn’t keep up with their likes and dislikes most of the time.
Ask them what they would like and try to keep their tastes in mind as much as is practical but make the food and give it to them. Always give them choices. If they don’t like some of it, then fine. They will not starve themselves even though it may seem like that sometimes.