Hume just tempered the importance of so-called “reason” in the process of decision-making. In fact, anything pretending to be “rational” (or “reasonable”) relies on passions, only less vivid ones:
The same objects, which recommend themselves to reason in this sense of the word, are also the objects of what we call passion, when they are brought near to us, and acquire some other advantages, either of external situation, or congruity to our internal temper; and by that means, excite a turbulent and sensible emotion.
For that matter:
The common error of metaphysicians has lain in ascribing the direction of the will entirely to one of these principles, and supposing the other to have no influence. Men often act knowingly against their interest: It is not therefore the view of the greatest possible good which always influences them.
That’s a one-two punch at rationalists: not only are they wrong on the nature of “rational” decision-making (they‘re not—it’s all about passions), Hume shows through a proof of the absurd that men, however abled with reason, behave in contradictory fashion. They therefore violate the most elementary law of reason, the law of non-contradiction.
Hume explains this perpetual state of contradiction through conflictual passions, which
guide command our decisions.
Why does a lover give themself feverishly to the loved one, sometimes at their own expense, without any assurance of receiving in return?
The lover wants the loved one because they are in love.[^raison-lysias]
Love is not a feeling of the order of reason. It is a passion, one among many other contradictory ones, which decisional weight would have been gravely neglected by the rationalists and metaphysicians.
Hume is an observer. He draws conclusions as simple as unshakeable from what he sees. Human beings are deeply irrational.
But this does not mean that love cannot be an affair of self-interest (where the lover is the main interestee, and even the only interestee, even though they give without counting), on the contrary; Hume writes on it later.