So, the story of Narcissus is a bit larger than this dope looking into a stream and falling in love with his reflection. The story of Narcissus is by the Roman, Ovid, in his epic The Metamorphosis. It's a pretty good story. Narcissus's is just one of several characters and plot lines.
There are two characters: Echo and Narcissus. Echo has been punished for some offense by being reduced to repeating the last few words she hears -- an echo. Echo's situation has been used as a medical term, too -- echolalia, where autistic children repeat whatever they hear. Some adults have this problem too -- Trump says something, and Republican dip shits keep repeating it.
Narcissus was out hunting with the boys. He apparently wasn't paying attention, or they deliberately slipped away. Meanwhile, Echo sees Narcissus and is stricken with love (or lust, or both) and wants to call out to him -- but she can't. Remember the curse on her? Fairly quickly it happens that Echo is able to come out of the bushes, and approach Narcissus. He's not pleased or interested. He's so uninterested that he tells her he hopes to die before he allows her to enjoy his (manly delicious) body.
Despite the harshness of his rejection, Echo's love for Narcissus only grows. What a nuisance! When Narcissus died, wasting away before his own reflection, consumed by a love that could not be, Echo mourned over his body. When Narcissus, looking one last time into the pool uttered, "Oh marvellous boy, I loved you in vain, farewell", Echo too chorused, "Farewell."
Eventually, Echo, too, began to waste away. Her beauty faded, her skin shrivelled, and her bones turned to stone. Today, all that remains of Echo is the sound of her voice.
So... what is it with Narcissus?
Maybe he is some sort of homosexual? [The sort of egalitarian relationships between men and women that are more common in the modern west were absent in Rome and Greece. To a large extent, "men composed society". The Greeks and Romans had attitudes toward sexuality that were somewhat different than ours.] A guy falling in love with the image of a male, his own or somebody else, seems kind of 'gay' to me. He's not at all aroused by the presumably beautiful Echo -- another gay feature. Gay guys usually are not excited by women. A lot of gay men tend to be attracted to men who generally look like themselves. People tend to eventually look like their dogs, too, but that's a different process.
Gay or straight, Narcissus is a sick boy. A sexual deviation that some young men (men in particular) experience is the self-involvement of excessive solitary masturbation. They apparently have a lot more than the average amount of tension to resolve--sexual or academic or something else. The main feature of narcissism is very excessive self-involvement, to the point of isolation. Perhaps it's a defense mechanism (escape from reality). Narcissists are not usually what one would call realistic about their own importance. (For many famous narcissistic people, realism would be the kiss of death). Donald Trump, again. He would likely find an objective appraisal of his talents and accomplishments devastating.
There are gay narcissists, though most of the raging narcissists I have observed have (presumably) been heterosexual.