What is necessary to understand before answering the question is that the stoics, like many ancient Greek thinkers, believed and pursued eudaimonia. From WP:
In the works of Aristotle, eudaimonia was the term for the highest human good in older Greek tradition. It is the aim of practical philosophy-prudence, including ethics and political philosophy, to consider and experience what this state really is, and how it can be achieved... Discussion of the links between ēthikē aretē (virtue of character) and eudaimonia (happiness) is one of the central concerns of ancient ethics, and a subject of much disagreement. As a result, there are many varieties of eudaimonism.
And this is important, because unlike religions which tend to prescribe behavior and focus on the afterlife (here are commandments, now live by them or suffer for all eternity!), the ancient Greek tradition of φιλοσοφία, philosophia advocated reason as a means to obtain eudaimonia. This dedication to reason over faith and dogma was as revolutionary to intellectuals as democracy was to politicians. This is still echoed by philosophers like Camus, who in his Myth of Sisyphus, argued against taking "the Leap" which is engaging in faith. He declared to take the Leap was philosophical suicide, and that the thinking man aspires to courage and reasoning as the basis for living life. With free will and reason, then, one simply must make choices between the good and the bad particularly in matters like love.
The stoics were a group of philosophers that extended into the Roman empire, and advocated using reason to achieve eudamonia by focusing on a set of fundamental virtues. From WP:
Stoicism is a school of Hellenistic religion founded by Zeno of Citium in Athens in the early 3rd century BC. It is a philosophy of personal eudaemonic virtue ethics informed by its system of logic and its views on the natural world, asserting that the practice of virtue is both necessary and sufficient to achieve eudaimonia—flourishing by means of living an ethical life. The Stoics identified the path to eudaimonia with a life spent practicing the cardinal virtues and living in accordance with nature.
Love, which is an essentially contested concept, can be quite a challenge to those virtues, particularly temperance. From the perspective of a naturalized epistemology, if the purpose of life is to survive to reproduce, then love which is intimately tied into the act of mating, is literally hardwired into our brains to be unreasonable. (For more information on that, read up on biological altruism.)
Epictetus and Love
Now, there is no extant work from Epictetus, whose influence survives only by those stoic thinkers who came after him. Therefore, it's not possible to explain his rationale in his own words. However, the general nature of your question and the fact that stoicism is an eponym that is a synonym for "detached" lays out a very obvious rationale. To a stoic, love in any form was to be chosen, not something that would be allowed to drive the choices of a thinker. And every choice is inherently a normative exercise: there are ethics and consequences and ethical consequences. And that means there are good and bad outcomes, good and bad choices.
"If someone is incapable of distinguishing good things from bad and neutral things from either – well, how could such a person be capable of love? The power to love, then, belongs only to the wise man."
Thus, if this fragment communicates anything, it is that a stoic chooses to love, and does so with reason. To declare the power to love to be under the purview of the wise is therefore a claim about the essential nature of love: it is a choice, not a compulsion. And this, this is the essence of what the virtue of temperance is about. From WP:
Temperance in its modern use is defined as moderation or voluntary self-restraint. It is typically described in terms of what an individual voluntarily refrains from doing. This includes restraint from revenge by practicing non-violence and forgiveness, restraint from arrogance by practicing humility and modesty, restraint from excesses such as extravagant luxury or splurging, and restraint from rage or craving by practicing calmness and self-control.
Thus, an act of love to a stoic must be a good choice coming from a place of wisdom. Only then will love allow for the fulfillment of eudaimonia. Since this more mechanical approach to love contradicts notions of love that Hollywood sells, an unrestrained passion where one is aflame with emotion, it might be difficult to see and approach like a stoic.