Two things to preface.
1) I think you're overthinking this.
2) overthinking is my specialty.
The question is, how do you dived something 0 times?
In the example you gave, you're not dividing the pizza in the first place. You're leaving it alone.
But if you divide by zero, you are required to cut the pizza, you can't NOT cut the pizza, but to divide by zero, you CAN'T cut the pizza, and then you have a paradox. There is no answer, hence why it's undefined.