why does a set of parametric equations need to be smooth and not cross itself in order to evaluate its arc length?

Question

My calculus textbook says that to calculate arc length of a set of parametric equations, the curve produced by the equations must be smooth and cannot cross itself. The book also defines smooth as the parametric equations have continuous derivatives that are never simultaneously 0. I completely understand why the derivatives of the parametric equations must be continuous: to satisfy the continuity needs of the integral over which arc length is evaluated. However, why must the derivatives of the equations never be simultaneously 0 and why can the curve never cross itself? Also, the not-crossing-itself necessity is not given for the arc length of a vector-valued function. Why are the two conditions for arc length different even though both evaluate arc length in essentially the same manner? Any help is greatly appreciated!