There could be reasons that it IS the case for her. I know when it was just my husband and me, before kids, it often felt less expensive to grab a sandwich out at a restaurant rather than cook. We'd get a nice salad somewhere and be done. It depends on what they are eating "out". We would go to The Loop (small Chicago style pizza chain that was inexpensive) and I'd get a burger and he'd get a chicken salad. We'd spend less than $15. And the food was GREAT. But, for me to make a salad at home, with all the ingredients, would probably cost $15 just for the salad...not including dressing or the burger. Why? Because you can't buy just ONE hamburger bun, or just enough lettuce for ONE salad, or a quarter of a tomato, quarter of a cucumber, a handful of olives, ONE carrot, etc... My husband also works (and did back then also) a very odd schedule, and often isn't home for dinner. So the veggies might not still be any good by the next meal. That half a tomato, would end up in the trash. Same with the half cuke, half onion, half bell pepper, etc.
And if the cost of the food items are relatively close, then why not? Because then you're saving on electricity you aren't using in preparing it. And you get your valuable time to relax and chat over your meal, instead of having to face the dirty kitchen when you're done.
It also can depend upon your tastes. My hubby is "finicky". He is a meat kinda man... (hold the potatoes). He likes his protein and his fresh veggies, and avoids starches (bread, pasta, potatoes, etc--- all the inexpensive things you can use to save $ when cooking).
So, maybe she isn't exactly right in every instance, but I think you could at least concede, that if you weren't feeding a family of 4, it would make more financial sense than it does to you now.