The big picture answer (because I'm on mobile and no expert) is "because colonialism".

The former colonies had been occupied for atleast a hundred years by the time they were given their independent status. During their occupation they were pretty much forbidden to grow their own food and could only grow cash crops and mine, which means when they were made independent they had to basically rely on what had been their colonizers to get basics like food and clothes. They were also restricted in their ability to trade with each other because (for the most part) there were no roads between African colonies, and there were no rail lines between them either, and the rail lines in Africa were all non-standard. Want to connect two rail lines between two colonies? Sorry, can't, the tracks are slightly didn't different widths, which means trains from one country cannot get onto a line from second country. Also, you'll have to special order replacements.

Under colonial rule Africans also didn't have much access to skilled trades, and nearly no access to educated trades. So, when they were made independent, there were few to no engineers or doctors. Once again, if you want those things, you're basically going to have to import them.

Colonial regimes had no concern for existing political boundaries. Tribes and nations were divided up between two colonies (and later states), and rivals were smashed into one colony. Add in that sometimes hundreds of tribes were merged into one colony, each one having their own language, and you don't have a recipe for political stability. Colonies in Central and South America had the dubious advantage of having their pre-colonial languages and tribal loyalties murdered out of them before they achieved independence.

And for the big one: tribal rivalry became a colonial weapon. Seen Hotel Rwanda? Right, that happened because the British used the minority Tutsi as a crudgel against the majority Hutu. Need someone to oversee the beating of an uprising of Hutus? Get the Tutsi to do it. When Rwanda was given independence, the hatred between the two groups went from "low level rivarly" before colonization to "screw it, kill all of them" after.

So, basically "because colonialism".