It appears what you (rocdocmac) are saying is:
Assume the pizza is a 2-dimensional circle (in a plane of Euclidean space). All cuts are straight lines (i.e., line segments).
The confusion that occurs is with the terms vertical and horizontal in the assumed plane, as they imply all vertical cuts are parallel to the imaginary y-axis and all horizontal cuts, if such were allowed, to be parallel to the imaginary x-axis. Yet, as the cuts are given to be in any direction, there was an implied contradiction to that inference.