First, there is no empirical evidence offered that the Church is responsible for this. All that is presented is that the Church opposes the use of contraception, which is true. What is also mentioned, but given no credence, is that the Church also opposes sex outside of marriage.
So we should draw the conclusion that the Latin American people follow the Church's teaching to the letter when it comes to contraception, yet ignore the teachings against fornication? It seems to me that the decision to fornicate comes first, then the decision whether or not to use a condom. So the Church is not in their thinking for the first decision, but then, between deciding to do the deed and actually doing it, they stop to ask "what would Jesus do"? And don't go back to revisit the first decision? The argument makes no logical sense.
Second, a UN official is quoted as saying:
"In Latin America the use of condoms has been demonized, but if they were used in every relation I guarantee the epidemic would be resolved in the region."
This is the lie that spreads the use of condoms around the world. The latex in a condom is dense enough generally to stop sperm from passing through it. It is NOT, however, dense enough to prevent the AIDS virus from passing through, rendering it useless in preventing the spread of AIDS.
A 2004 study titled Condom Promotion for AIDS Prevention in the Developing World: Is It Working? (Studies in Family Planning 2004; 35: 39–47) found that:
"In many sub-Saharan African countries, high HIV transmission rates have continued despite high rates of condom use." In fact, they continued, "No clear examples have emerged yet of a country that has turned back a generalized epidemic primarily by means of condom distribution."
No surprise, then, that Botswana, Zimbabwe, Kenya, and South Africa — the nations with the highest levels of condom availability — continue to have the highest rates of HIV prevalence ("The White House Initiative to Combat AIDS: Learning from Uganda," Joseph Loconte, Executive Summary Backgrounder).
This article also mentions an example of AIDS declining in Uganda:
Uganda at one time had the highest rate of HIV/AIDS in the world. Starting in the mid to late 1980s, their government instituted a program to teach abstinence before marriage and fidelity to one's partner afterwards. They only reluctantly advised condoms for high risk groups (like prostitutes) whom they knew would not accept the other two approaches.
In 1991, the prevalence rate of HIV was 15%. By 2001, it had dropped to 5%. It was the biggest HIV infection reduction in world history.
When you read these kinds of articles, do so with a critical eye. The UN and the mainstream media are no friends of the Catholic Church. But Jesus Christ is the Way, the Truth, and the Life. And the Truth will set you free.