I don't understand the premises of Hume's argument against moral rationalism if someone could explain it to me please.
The moral rationalism with which Hume is concerned in the Treatise is roughly the view that reason can both ascertain the proper (morally correct) goals of action and motivate us to pursue - to act on - them. In effect you ask why, on what grounds, Hume denies that even if reason could ascertain the goals of action (which it can't), it could not motivate us to act on them; so you are concerned with the motivational inertness of reason.
The best-known texts from Hume on reason's inertness come from Book 2 of the Treatise , where Hume first offers his argument for the conclusion that reason by itself is motivationally impotent. At T 2.3.3 (SBN 413-18), "Of the influencing motives of the will", Hume argues for his conclusion by examining the two roles of reason - demonstration and probable reasoning. He argues that demonstration is not motivating by itself, because it deals with logical and mathematical relations between ideas. The role of probable reasoning, he then explains, is to figure out what objects are causally connected to what we desire or to what we are averse to. But probable reasoning does not originate motives because: 'Tis obvious, that when we have the prospect of pain or pleasure from any object, we feel a consequent emotion of aversion or propensity . . . 'Tis also obvious, that this emotion rests not here, but . . . comprehends whatever objects are connected with its original one by the relation of cause and effect. Here then reasoning takes place to discover this relation; and according as our reasoning varies, our actions receive a subsequent variation. But 'tis evident in this case that the impulse arises not from reason, but is only directed by it. (T 188.8.131.52; SBN 414).
(Elizabeth S. Radcliffe, 'The inertness of reason and Hume's legacy', Canadian Journal of Philosophy, Vol. 42, No. S1, Special Issue: Hume in Alberta: Selected Papers from the 2012 Hume Conference in Calgary (February 2012), pp. 117-133: 118. 'SBN' refers to Selby-Bigge's edition of the Treatise, revised by Nidditch, 1978.)
The quotation from Hume (''Tis obvious, that when we have the prospect of pain or pleasure from any object...') could be clearer, so let's make it so. What Hume has in mind is that if, say, we see a delicious apple hanging out of reach on a tree, we have 'the prospect of pleasure', but how do we get the apple? 'Probable reasoning' has not led us to desire to eat or possess the apple but it can serve the instrumental purpose, 'by the relation of cause and effect', of working out how to obtain the apple - for example, by using a ladder.
Overall the implications for morality are plain. Reason, which deals with logical and mathematical relations between our ideas, cannot determine what we ought morally to do - cannot set the goals of moral action because such goals are not ascertainable by logical and mathematical relations between our ideas. Equally the knowledge of logical and mathematical relations between our ideas cannot motivate us to action. For motivation, desire or emotion is required.
It is the same if we equate reason with probable reasoning. By such reasoning we can calculate means by which to pursue our desires but probabilistic reasoning cannot motivate us to action since it cannot instill any desires, specifically desires to pursue the proper (morally correct) goals of action, in the first place.