Well first you'd send a flight of 4 fighters from Mt Pleasant to challenge a Sea Harrier CAP. 4 vs 2 means the outcome would likely favor Argentina. Do that a couple of times and soon enough the Sea Harrier CAPs will have to double up. So now shuttle in a few more fighters from the mainland and send 6 or 8 fighters to challenge the Sea Harrier CAP (6-8 vs 4).How would an all out attack on the RNs Sea Harriers and GR3s take place, its not as if they were all in the air at once for most of the war? After the initial May 1 strikes on Port Stanley and Goose Green airfields the RN settled into proving a CAP or 2 for the daylight hours. This is a big ask for 10 pairs of aircraft, declining to 8.5 pairs, with a 75 minute flight endurance.
Within a couple of days the RN would have to choose between pulling back its CAP aircraft or finding a way to neutralize Mt Pleasant. Pulling back the CAP would significantly reduce their ability to continue with the landings. Historically they were not very successful at neutralizing Mt Pleasant. On top of that any increased attrition to the Sea Harrier force would significantly impede preparations for the landing, and lack of air dominance would make it a lot harder to intercept strikers once the landings did happen.
But all this hinges on fighters being able to operate from Mt Pleasant (i.e. low take-off & landing speeds, brake chute, no complex electronics), with a missile better than AIM-9B (e.g. Magic 1) and a climb rate similar or better to Harrier. They didn't have that but it wasn't unachievable.