The stick back instruction is for the reasons suggested by Airbedane above. If you follow the instructions in the POH, you will stop the rotation quickly and recover with minimum loss of altitude.
However, the Robin will recover nicely from a spin even with the stick fully forward. If you are want to do a competition spin, with a vertical exit, you'll probably find it better to use forward stick. The rotation takes just slightly longer to stop, but your attitude on exit will be much closer to vertical and you will score more points if being judged!
I haven't flown a Robin 2160 for some time, but I seem to remember the POH mentions that the "stick forward" recovery can be used, but is not as quick as with the stick back.