The secret is to cook them for the appropriate length of time, to use the right method, to season them, etc. for instance a vegetable that a lot of people claim to dislike are sprouts, but most people either overcook them, or undercook them, which can cause them to taste raw or bitter. The trick is to cook them so they’re just tender enough to bite through comfortably, but to still have a little texture, this way they’ll be sweeter. You can also do things like roasting them with some oil, which will cause their natural sugars to release even more, the same goes for lots of vegetables, like you mention only liking carrots when they’re mushy, but have you tried roasting them with some butter? You can also add some honey and herbs like thyme to them. And going back to the sprouts, you can cook them until almost tender and then sauté them in a pan with some bacon. It’s also important to season vegetables with salt and pepper, just like you would a steak, even to season the water if you boil them is vital, or to add things like herbs or garlic to things like potatoes for extra flavor. Finishing vegetables off with butter also is important to maximise their flavor. Like just new potatoes boiled in salted water until tender and then drained and seasoned with salt and pepper and served with some butter mixed through them is amazing, even adding some chopped chives can take it to another level. There’s so many things you can do with vegetables.