Narcissus was a 16 year old boy who just wanted to be a hunter. Much like the goddess Artemis, he wanted to live in the forest and eschew all romantic and sexual connections.
He may have preferred isolation because he was famous across all of the Hellenic world for his great beauty. And no matter how many people asked this teenage boy for his hand in marriage or to have intimate relations, he refused.
There was one man, Ameinias, who would propose marriage to Narcissus again and again. He wouldn't take no for an answer. One day, narcissus got completely fed up with it, and gave Ameinias a sword. He told the sexual harasser to go kill himself.
Ameinias did as he was told, and stabbed himself in the heart with the sword. But before he died, he prayed to Nemesis, "Though he should love, let him not have what he loves!" Nemesis agreed.
Narcissus loved nobody, at least not romantically or erotically. But after Nemesis agreed to Ameinias' prayer, he noticed his reflection in a pond. Recognising himself for the first time in the way other people saw him, he became infatuated. Narcissus had neither food nor drink for the rest of his life. He simply sat and stared at himself until he died.
When he died, the nymphs of the forest, who loved him, grew flowers around his body. Narcissus flowers.
Nemesis is the goddess of punishment for hubris. She punishes mortals who think they're better than the gods. Why would she punish Narcissus?
My theory is: The ancient Greeks (and their gods) were so aphobic, they thought if someone didn't want to have sex, it's because they think they're better than everyone else.
I recognise that aphobic Greeks and aphobic westerners have lied to you about this myth. But Narcissus is our history, as asexuals. This is what people thought of us for 2,000 years. And it needs to change.