Three factors that played a role in bringing about the slave trade across the Atlantic. Surely this doesn’t explaind everything, but it is a good starter.
A Tale of Supply and Demand
The demand for labor increased through: exotic products (i.e. tobacco); luxury niche products (i.e. gold.) As a result, labor demand increased.
At the same time the supply of labor decreased. There was a decline of the Amerindian population. European migrants and indentured servants only limited. In Europe nobody was forced to migrate (except prisoners and convicts.)
There was a strong demand for labor in the Americas due to the demand for plantantion produce and precious metals. The African Slave Trade was a welcomed opportunity to expand and yield more tropical products.
Why Africans and not Europeans?
There is a certain paradox that Africans, and not Europeans were taken as slaves. Africa is distant, there is little infrastructure and those that advanced the trade did not have much influence there.
So why enslave Africans?
There is a certain cultural and physical alienation, so it was an easier rationale for society to morally justify the trade. There were also plenty of African leaders that were willing to supply slaves. And where there was a seller, there was a buyer. As a result of revolution in ocean-going technology, Europeans could fetch slaves from distant locations and move them over long distances.
The slave trade was thus a product of differing constructions of social and the ocean-going technology that brought Atlantic societies into sudden contact with each other.
Africans started to enslave their own people. And they were prepared to sell as many Euro-American plantation owner were prepared to buy.
Unfortunately African resistance was not strong enough. Only about one in ten slaving voyages experienced major rebellions, which only had the effect of increasing the cost of slave voyages. It did not stop the slave trade. Additionally Europeans just avoided regions such as Senegambia, Sierra Leone, and the Windward Coast where rebellions were more likely to occur.