Reason you shouldn't is the wheel width on the ABS is a half inch (?) bigger than the non ABS wheel, so the 120/70 is designed for a wheel of the ABS wheel size. Tire fitment charts will show this.
However, whether you shouldn't and whether you can are two different things, as many, many, including myself, have used the 120/70 with no issues, on the non ABS wheel. Your speedometer will not be as accurate though, showing you travelling about 6 mph faster than it would read with the 110/80 tire.