Because Australia in 1900 was a highly racist society composed of recently joined-together and often-fractitious individual states, with an economy hugely dependent on primary production, most notably of a single product (wool) which was entirely dependent on foreign demand for its sources of income. It had a recently-written constitution which was largely based on that of the United States of America, had the basis of its legal and property system in the English common law with a few local modifications, and the rest of its core cultural traditions likewise stemmed from the British Isles. It had a system of unfree labour which was abhorred by much of the world.
Replace Australia in 1900 with CSA in 1865, and wool with cotton, and the description doesn't sound that far off...
Now, granted, there are certainly differences. To name but one, the slavery in Australia was only in a part of one state, and technically illegal. But still, it seems a much stronger comparison than anywhere in Latin America. In those countries, slavery was illegal (except for Brazil, and Brazilian slavery is actually quite difficult to compare to Confederate slavery). And they had a vastly different legal and cultural tradition, particularly in terms of their attitude to property rights and the legitimacy of government, which is the thing which usually sends countries on the slide to banana republic territory. Other than geographical proximity, I'm not even sure why people want to compare the CSA to anywhere in Latin America, except Brazil. And even Brazil isn't that close.