Matlab's bode somehow finds a way to examine the transfer function and so to determine the best range the phase should be placed at.
Mathcads arg function doesn't know anything about the transfer function - its simply receives a complex number and returns its argument, the angle, and this will always be in the range (-pi; +pi]. This range is as good as any other and its similar to the atan2 function. And thats also the reason you get the jump up to +180° step when the angle would go below -180°. "arg" would never give you an angle below (or equal to) -180°.
Easiest solution is to write an alternative "arg" function which returns the angle in a different 2 pi interval.

Put it at the top of the sheet (maybe in a collapsed region).
Or you may use an all-purpose "Arg" function where you can choose the start of the 2pi interval as its second argument:

The drawback of these simple solutions are, that you have to determine and chose the range for the angle manually yourself and that they only work OK as long as the range of angle values does not exceed a 2 pi interval.