First of all, we must be sure not to speak of this as if humans in Africa said to themselves "let's leave Africa and go somewhere else." They would have had no idea that they were leaving Africa because Africa is an idea that modern people have come up with, not a truly natural fact.
The early humans who left Africa did not do so knowingly. Instead, they were just migrating, probably very slowly, along with plants and animals that they used for food. They would have just been moving along with their food supply so as to be able to survive. Eventually, their movements took them around the globe.
The early modern humans who migrated out of Africa did not do it on purpose or with any intent. They were just moving along with their food.