Seems the Star Alliance planner wants you to fly via Frankfurt or Johannesburg.
SIN-JNB-EZE: 10,458 miles
SIN-FRA-EZE: 13,526 miles
SIN-LAX-IAD-EZE: 16,289 miles
To route via LAX would add an additional 5,831 flying miles as a bare minimum on top of the most direct route. Other than AC via YYZ, which would mean an even bigger detour, the only other Star carrier to fly to EZE from within the USA is UA from IAD.
You may have to do two redemptions for this one should you wish to route via North America.