The whole story is that Narsissus was ridiculously handsome and any woman would be overjoyed to have him. But he was way too busy enjoying nature, hunting and doing other non-sexual stuff to start a relationship with anyone.
Then the nimph Echo fell madly in love with him, but he didn't care much about that. So, in unrequited love she fled to a cave where she wanted away, only her voice remaining.
Depending on which myth you read, either this, or him denying some other woman is why Aphrodite decided to punish him to fall in love with his own reflection in the stream. Which is doubly insulting, since Narsissus' dad is basically the god of rivers.
The point is, he was aromatic until he was cursed by the gods for it.
Actually, it was Nemesis, the god of divine punishment for hubris. Nemesis' job is to punish any mortal who thinks they're the equal of the gods. And in Greek society, asexuality and aromanticism were so villified that not dating anyone was equated with thinking you're equal to the gods. It's a nonsense stereotype kind of like the American/English stereotype that trans women are sexual predators.
When Narcissus was born, an oracle warned his family "This boy will die if he sees his reflection". But it's unclear whether Narcissus falling in love with his reflection is a natural character trait, or something Nemesis cursed him with in addition to showing him the spring. It would have looked the same either way to the oracle. Either way, Nemesis knew she was killing Narcissus on purpose, just to answer the prayers of an incel who was mad he wouldn't date them.
Other fun facts: Narcissus was 16 when all of this happened. He was 16, and society already thought he owed other people his love or he should die.