Unfriendly staff

I had booked an air flight to leave King Shaka international airport this morning at 7:40. I arrived at the airport at this morning and stood in the line while there was only 3 people helping to check in people. I got the lady who was the most unfriendly in the world, to just say that the flight is boarding and we not allowing you on. I honestly don't understand why must the boarding gates close 40 minutes before the flight takes off. Please can someone contact me to arrange a full refund for my 2 tickets and I always fly with SAA but after this, I will never fly with SAA again...