I do find a blanket “I don’t eat vegetables” statement odd mainly because there’s such a HUGE variety of vegetables and ways to prepare them. For example, a green salad vs cream of butternut soup vs lemony steamed broccoli vs buttery parsnip mash vs maple-glazed carrots vs a spinach croissant all seem quite different to me. I’d think: c’mon, you must like SOME vegetables!
But then, I don’t eat red meat or pork/ham. Someone who loves these might say the same to me: there’s such a variety - hamburgers and filet mignon and meatloaf and bacon sandwiches and hot pot and baked ham and pepperoni pizza and lamb kofta and croque monsieur and Salisbury steak and biltong and chili cheese dogs..! 
I cook vegetarian at home, so lots of things would be difficult to make without ANY veg, like curries, chili, stir-fry, quiches, soups, stews, vegetarian lasagne/filled pasta, tacos, etc. When I’m cooking, if someone wants to skip vegetable sides, fine, and I don’t mind avoiding a particular ingredient that I know someone dislikes. But a complete ban on ALL veggies for meals I cook would be very hard to stick to for me; they’re in everything!
I also think sometimes people who aren’t that into food or cooking use “vegetables” kind of generically. For example, I’ll often make roasted whole tomatoes or a tomato salad and they function as a vegetable even though they’re technically a fruit. Aubergine, too. Similarly grains like corn, or pulses like edamame. On the other hand, I never really think of potatos as a vegetable, but they are. So perhaps worth clarifying what “no vegetables” means to this specific person?