The "dueling speeches" bit attracted a lot of attention, but Congo had problems that went much a lot deeper than that.
-- We all know about the "less than 30 college graduates in a country of 20 million" bit. Less well known, but arguably more disastrous, is that there were less than 5,000 /high school/ graduates in the whole country. The Belgians had quite deliberately set out to educate most of the population to around a sixth grade level; they wanted people who had basic literacy and numeracy, so they could be good workers. But higher education (beyond 10th grade) was firmly discouraged.
The Congo thus reached independence without a single Congolese doctor, lawyer, accountant, or engineer.
-- No Congolese had any experience with running a government, or indeed with running much of anything. Up to 1960, no Congolese had been allowed to run for political office, be an officer in the military, organize a trade union, or own a business larger than a middling big shop. Neither Lumumba nor anyone in his cabinet had ever been allowed to run anything bigger than a local post office.
-- There had been no nationwide elections in the Congo until the eve of independence. In fact, no blacks had ever voted for anything at all until 1957, when a handful were allowed to vote in carefully controlled municipal elections. (This was actually an experiment about giving a little power to the small white settler community; a few blacks were included if they passed property qualifications, which of course most didn't. Note that the Belgian Congo had no tradition of election even for whites.)
-- The new government was riven by ethnic and ideological divisions that pretty much ensured it would be unworkable even if everyone involved had been Madison, Jefferson, Hamilton and Adams.
-- The new country also had some fairly vicious ethnic divisions, which had been papered over rather than resolved by the Belgians, and which in a couple of cases were quite deliberately exacerbated by the Belgians.
-- The Belgians had quietly removed the colony's gold reserves from Leopoldville as soon as independence talks got under way, thereby ensuring that an independent Congo would have nothing to back its currency with. And then -- true story! -- as soon as independence was declared, they declared the Congolese franc inconvertible with the Belgian franc... because, you know, the Congolese franc wasn't backed by anything.
The Belgian system was designed to fail catastrophically if Belgian rule was ever removed. This was a feature, not a bug.
If you want to have a better independent Congo, you have to either make dramatic changes to the nature of Belgian colonialism, or -- more likely -- go back before 1908 and give the colony to someone else.
Doug M.