SAA REFUSAL OF BOARDING WITHOUT ANY RECOMPENSE

I would like to complain about being denied boarding on my return flight from Mauritius to South Africa . To date I have not received a reasonable excuse for why this was . I was told that the airline reserve the right to do so. I was also informed that I was late for boarding although I was there 15 minutes before the airplane left. I did not receive any last call for boarding or kind of compensation for this . The reason why I was at the boarding gate a little bit late was due to traffic and being held up at the Immigration point and then again the traffic at baggage control. There was no consideration or special concession given to us and thus I have just lost all the fare that was paid for this flight ! I was then prompted to buy tickets for the next available flight . I need reasons, i need to know who occupied my seats on the plane , how fully or empty booked that flight was , what the legal recompense for the loss of air fare, the loss of work for one day , the additional cost of travel and accommodation, the loss of child care . None of these factors were taken into consideration when I was refused boarding on to a flight that I was there to board before it left.