How to explain to my wife that she can't eat like me and lose weight?

You need to explain to her that because you do a lot more physical activity than her, your body uses up a lot more energy taken in through the calories. Therefore, you need more proteins, carbs, fats, and basically more calories overall. Because she's probably smaller than you and less physically active, her calorie consumption should be less. If she really doesn't want to be more physically active, for whatever reason, tell her she can start by cutting down her calorie intake (and by taking in more "healthy calories"), but it should most definitely be less than what you eat because she'll end up gaining weight by not using up the energy provided by those calories.

There is a Coursera offering at the mo called "Designing Your Personal Weight Loss Plan". Maybe suggesting she sign up to that would be a good, nonjudgmental, way to get the information across.