SAA plans to cut the route next year in favour of maintaining other loss-incurring routes to among others, Brazil and China, which are fellow members of the BRICS economic alliance of influential emerging economies.
Bryer says SAA has not been entirely clear on why it has chosen to cut this particular route when there are others around the world that are making losses as great, if not greater.
"The issue is capacity. The bulk of the passengers coming via São Paulo in Brazil are corporate travellers, many destined for the oil and gas enriched countries to the north of South Africa.
"Cutting the Buenos Aires route means there's going to be a capacity shortfall for leisure travellers and SAA has not explained how it intends to make up for this, which is especially worrying considering how much money South Africa has invested in the past three years in aggressively marketing this country as a leisure destination in Brazil.
"If SAA is intent on cutting this route that might be seasonally profitable, surely the short-term answer then is to increase the number of flights from São Paulo?
"One has to question now whether that money was well spent if we're going to dramatically cut the number of flights with which South American leisure travellers can actually get here."
Bryer says SAA are not demonstrating sound reasoning, since the impact of the decision will also affect a far greater area than just South Africa.
"OR Tambo International Airport is Africa's most important inter-continental transport hub. Last year there were nearly 600,000 transit passengers through SA's borders, most of them passing through the portals of this one airport, destined for other parts of Africa.
"And that's not counting those South American travellers who spent a few days in this country before proceeding to their next destination," says Bryer.
"Doing away with this route effectively kills numerous tourism and trade opportunities for so many countries to the north of our border, never mind the negative effect on the South African tourism growth potential and the loss of revenue for our economy."
Bryer says like much of Latin America, Argentina's economic growth for 2014 is pegged at around 3%, which is a radical deceleration from the noughties boom period, but still a reasonable outlook in global economic terms despite high inflation rates.
"People from South America travelling to Africa increased tenfold year on year and thousands of them are passing through the airline hub that is Buenos Aires.
"The number of South and Central American incoming passengers rose by 37% last year compared to 2011.
"President Zuma was quite right when he announced these numbers in April this year in saying that much of this growth was as a direct result of actively marketing South Africa as a destination in Brazil," says Bryer.
"So surely the sound economic decision for South Africa and Africa as a whole then is to expand that successful marketing campaign to other countries in Latin America to grow those markets, rather than simply cutting us off at the knees?," Bryer says.
