Another question you may also ask is, why we are using the vertical distance as error and not the horizontal one or, even better, the perpendicular one (guess this would be fun when we include units). Think the answer is - because its easier!
The assumption is that there is an independent variable and a dependent variable, and the independent variable has no error. By convention the independent variable is plotted on the abscissa, so the errors are "vertical".
If both variables have errors, it's still possible to do a least squares regression, but not by using any built-in function in Mathcad. It's also possible to do a least squares fit with the errors always perpendicular to the fitted curve. I have a nice example worksheet (not written by me) of a parametric least squares fit to an ellipse, in which the errors are always perpendicular to the ellipse.