One factor favouring southward movement may have been environmental change that is thought to have created easier routes trough the forest in the last millennia BC (summarised here). It’s still unclear which route was taken – perhaps both – or even whether the western and eastern lines of advance diverged before or after the forest (genetic evidence for a "late split" is presented here). The Adamawa-Ubangian-Zande language groups are thought by some to indicate eastward movement from eastern Cameroon north of the main advance, though the affiliation of these non-Bantu tongues remains uncertain.
But weight of numbers would alone have tended to direct the movement south, While the peoples of West Africa may have numbered a million or more in the second millennium BC, those undertaking expansion beyond the traditional homeland were only a part of the hundred thousand or so occupying the eastern Nigeria-northwestern Cameroon area from which the movement originated, or even of the smaller number around the Bamenda highlands whose environs appear the likely starting-point – no match for perhaps two million in Egypt or ½m-1m apiece in Sudan or the Horn.
The difference in land-use intensity and resulting population densities means that it would have been easier to expand into regions of sparse hunter-gatherer occupation to the south and southeast than other areas of existing agricultural or pastoral settlement. While the mechanics of the movement are unknown, farmers could establish themselves to the south without damaging conflict with existing communites, which just wasn’t possible in northeastern Africa except around the uppermost reaches of the Nile: farming and gathering communities coexist to this day in parts of the forest belt and beyond, though there has also been subjugation and abuse of the area’s earlier inhabitants.
To that extent “migration” is something of a misnomer, and we should think rather of ripples of expansion through tentative forays by the latest subgroup of each successive frontier settler population into more sparsely-inhabited adjacent zones, in which the number on the move was (at least until the emergence of large kingdoms in more recent times) only a small fraction of the growing total speaking Niger-Congo languages.