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The continents that are most bothered about this are the continents that are dependent on these African countries for their natural resources. Take for instance, France, which is already slowly being affected by the limited resources they are no longer receiving from the country they have been exploiting. From Burkina Faso, they have suspended all gold exports to France.
If there are more coups and resources to European colonizers are cut, many of those European countries will be affected. That is a danger for their economy.
And what is a danger to a western economy, is a danger to the regime in whatever country is causing it. I am sure we will soon start hearing more talk of the lack of democracy in certain African countries, and how we need to do something about it. Think of all the poor people down there that are being tyrannized.

Liberation is what Africa needs and even though we claim to be in a civilized world Africa resources are being exploited and some times even at the cost of African lives.
Although the civilian government has left many African countries in a big mess let's not forget that African countries has had military rule and it was even worse.
To be sincere it is not about if the ruler is a civilian or a military personnel it is about the individual that rules. When the leader has the interest of the people at heart that is when Africa will grow.
Freedom must be given, and aid must be lowered or completely eliminated. Africa needs to stand on its own feet, and not rely on the help of others. Only this way can it develop and prosper.