You people don't really know what the Z axis is, do you? X is left-right, Y is up-down. Z is a corkscrew motion.
Cute, but wrong.
Typically the Z axis is that axis which is perpendicular to both the X and Y axes, but which axis is which depends on the conventions of a particular usage. For instance, on a computer monitor, the X axis is horizontal, the Y is vertical, and the Z is into
the screen. In algebraic geometry Z is the vertical axis. With regards to aircraft and spacecraft, X is the nose to tail axis, Y is the left to right, and Z is the up to down (so Kirk's order is correct relative to the Enterprise in TWOK), unless you're talking Yaw, Pitch and Roll, in which case Z is the roll. But what X, Y and Z are all depends on what you're talking about as to which axis is what.
So next time you choose to lecture someone, take a moment to check your own command of the facts first.