I've had mainly 3 reasons to switch to R:

(1) It's free

(2) It has a huge repositoriy of libraries. There's hardly anything that you can't do with R. In my special case it was about hazard-rate models, which are barely implemented in other tools that I tried (namely EViews, SPSS)

(3) It has a BIG community behind it, which you can ask for help once you're stuck. I haven't found this kind of "service" in other software (namely, again, EViews).

Because Mathematica costs at least $2000+ and R is free software. That makes R more suitable for teaching purpose.

Almost the only reason you'd need to use R. I cringe when professors ask their students to use non-free software when equivalent or better free alternative exist.