So just eat the pizza. Not the whole pizza, just a slice or two.
Seriously, by itself, what is wrong with eating pizza?
if you are on a low carb diet, you are physiologically changing the way your body fuels itself. Eating minimal carbs for a few days (20-30g) while eating lots of fat and protein causes your liver to start producing ketones which burn fat to fuel the body. When you eat a normal amount of carbs (100g+/day) your body creates insulin to convert the carbs to glucose, also known as an insulin reaction. No matter what you eat your body is creating insulin, but on a low carb diet with ketone production the insulin level is very low and steady and your body is mostly using fat for fuel, whereas with a regular carb diet you have insulin spikes (blood sugar levels is another term) related to food intake.
I should say in both cases the protein you eat is used for maintaining (or building) muscle mass, with carbs (glucose) or fat (ketones) used for other energy requirements, which is why as you approach more optimal body weight levels (or stalling on weight loss) it becomes important to figure out exactly the macronutrient levels you need to lose or maintain weight - X amount of calories used at Y weight (BMR), and a percentage mix (usually around 60/35/5 of fat/protein/carbs) to support that. There are online calculators like
http://keto-calculator.ankerl.com/that let you calculate the exact macros for your weight, height, etc.
So thats why those who are obese and on a low carb (keto, atkins, lchf) diet shouldn't eat a slice of pizza, the amount of carbs would "kick" you out of keto by producing a lot of insulin to convert the carbs and stopping the production of ketones until the insulin reaction has subsided. You can re-enter ketosis within a few hours or a day or two of eating a lot of carbs, but you have halted your progress until that process is complete.
The biggest thing about a keto diet is not the way the math works out on energy consumption, but the idea that by eating mostly fat/protein you satiate yourself much faster than with carbs, you stop developing cravings for sweets/breads/pasta after a week or two (usually), and end up over the long run being able to eat well within your calorie limit while not craving carbs/sweets (blood sugar spikes).