'Tis not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. 'Tis not contrary to reason for me to chuse my total ruin, to prevent the least uneasiness of an Indian or person wholly unknown to me.
His point is fairly simple. Hume is an empiricist of the early modern period, which means that he shares with Descartes the peculiar view that human consciousness constists of impressions and ideas that act something like images on a screen. Unlike Descartes, Hume holds that all of these impressions and ideas have their origins in sensation, and that reason is and must be utterly passive.
Given the assumption that reason is passive, it seems to follow that reason cannot intervene in shaping or even judging action. Everything has to begin and end with some sort of impression - in this case a moral sentiment.
But sentiments are tricky things.
There is also the problem that Hume sometimes seems to smuggle a free agent into the Cartesian theater, willing and choosing like the most Kantian of moralists . . .