So this question is very complex and relates to questions of development economics, colonial history, and geopolitics. The short answer is that there is no single rationale for Africa's present relative underdevelopment, but there are a number of contributing factors that when combined provide the beginnings of a working hypothesis.

First, it is notable that Africa has not always been underdeveloped. Rather, its relative underdevelopment came about in the last few centuries. The oft-cited richest man ever was Mansa Musa, a king of Mali in the middle ages. North African and Central African kingdoms grew prosperous off of trade of gold and salt, valuable commodities at this time in world history. A rough sketch of historical GDP per capita is found here https://imgur.com/a/vqp4hYv. The data comes from Economic Historian Angus Maddison's report for the OECD on the history of worldwide economic development. As you can see, Africa as a whole maintained developmental parity up through 1500, at which point the parts of the world now known as more developed (Western Europe and North America in particular) began to accelerate, with the gap widening post 1820. This process is called the Great Divergence, and represents the wealth that flooded into the Western World from colonialism and industrialization.

However, Africa remains by and large less developed than even other countries left out of this development of wealth, specifically Latin America, non-Japanese Asia, and Eastern Europe. There are two developmental gaps: the gap between Africa and the More Developed Countries, and that between Africa and the rest of the Less Developed Countries. The first is simple enough: colonialism and industrialization made Western Europe and parts of North America astronomically rich compared to anything in prior human history. The second has many hypotheses and confounding variables.

One major one, as your friend mentioned, is the legacy of colonialism/imperialism. Between 1880 and 1914, nearly all of Africa came under European control. Colonialism and imperialism were particularly harsh in parts of Africa, with Africa's natural resources being extracted to Europe. There is little doubt that this process of exploitation had a permanent impact on the economies of Africa. While the sum total of taken wealth may never be accounted for, it has definitively reduced African development. I'm going to specifically address your note here about the "good parts of Africa". This largely relates to differing strategies of colonialism. Colonialism around the world has historically taken two separate strategies: settlement and exploitation. In the settlement strategy (see: the British 13 colonies, South Africa, French Algeria, sort of Argentina), large numbers of settlers from the Mother nation would settle in that country, and make it a sot of extension of the homeland. In the exploitation strategy (see: the Belgian Congo, Peru, the entire Caribbean), the entire goal of the colonization was to take resources (especially gold) and bring the generated wealth back to the home country. Economists Daron Acemoglu, Simon Johnson, and James A. Robinson in The Colonial Origins of Comparative Development: An Empirical Investigation compare the usage of these two strategies with later development and find a substantial correlation: former colonies where settlement occurred tended to have better post-colonial economies. This potentially explains the reasons that areas with more mixed race people may have better Economic outcomes.

I touched on colonialism in terms of resources above, but it's also key in the next major hypothesis: structuralism. In particular, African colonies typically had very little institutional development (e.g. having a central bank, a functioning bureaucracy, powerful local governors). Thus, in the wave of decolonization post-WWII many African nations struggled to construct a state, especially given the borders of the states were drawn very arbitrarily. This hypothesis argues that economic development shortfalls post independence are best explained by the lack of institutional memory. Contrast China, with a bureaucratic lineage and a united state stretching back thousands of years, with the Democratic Republic of the Congo, where the country itself is largely artificial. The rushed process of decolonization quite possibly exacerbated preexisting economic disparities, and likely helped to lead to the numerous economy-sapping instabilities that have occurred in Africa post-1945.

Furthermore, there is a differential level of investment that has occurred historically in Africa. Some development economists (e.g. Jeffery Sachs) argue that the main reason Africa is underdeveloped is because all of the other regions have had major western investment at some point in the recent-ish history. Asia, for example, saw foreign investment skyrocket during the Cold War, as did Latin America and Eastern Europe. Sachs in particular argues that investment in Africa, such as that China is beginning to engage in now, would be able to result in vast improvements in economic fortune relatively quickly.

Lastly, I'd be amiss if I didn't mention the resource curse. The resource curse argues that since Africa has historically relied on natural resources for nearly all of its wealth, it makes it more difficult for it to develop. For example, China's development is largely due to its growth in Manufacturing, while India has focused on IT. Africa still relies on natural resources, which are both very volatile in price, and prone to political instability. These combine to make development more difficult. Historically, nations with large amounts of natural resources have tended to have lower rates of economic development and diversification, due to limited incentive to branch out. This hypothesis is not deterministic, as many nations have "overcome" it, but it is quite possibly a contributing factor.

I've largely touched on an economic history explanation of African underdevelopment. There are many other contributing factors, such as geography (Africa is largely landlocked, with poor rivers and a huge desert in the middle of the continent limiting trade), economic policy both at the country and international level, and persistent conflict, but I hope this gives you a bit to go off of.

Some further reading/more sources:

Innovating Development Strategies in Africa: The role of International, Regional, and National Actors (Landry Signe)

Africa's Development in Historical Perspective (Emmanuel Akyeampong, Robert H. Bates, Nathan Nunn, James Robinson)

Economic Growth and Development in Africa: Understanding Trends and Prospects (Hormon Chitonge)

Escaping the Resource Curse (Macartan Humphreys, Jeffery Sachs, Joseph Stieglitz)

Commodities and Capabilities (Amartya Sen) (not about Africa in particular, but useful nonetheless).