Asexuality in men was often portrayed negatively in Greco-Roman myth, as Greek and Roman men were expected to marry and continue their family line. Just as Hippolytus' rejection of Aphrodite / Venus / physical love was punished, so too is Narcissus punished for his rejection of Echo. Narcissus is often coded asexual by various authors, as he rejects all men and women suitors (not just Echo). His 'love of himself' is a symbolic rejection of romantic and physical love.
Se Narcissus amat captus lenonibus undis.
Cui si tollis aquas, non est ubi saeviat ignis.
Captivated by the still waters, Narcissus fell in love with himself.
But if you removed the water, he wouldn’t be burning with love.
--Codex Salmasianus 219
Invenit proprios mediis in fontibus ignes
Et sua deceptum urit imago virum.
[Narcissus] found fire in the midst of water
And his own reflection burns for a deceived lover.
--Codex Salmasianus 145
Ardet amore sui flagrans Narcissus in undis,
Cum modo perspicua se specualtur aqua.
As he catches sight of himself in the clear water,
Narcissus burns for love of himself.
--Codex Salmasianus 146
Dum putat esse parem vitreis Narcissus in undis,
Solus amore perit, dum putat esse parem.
Narcissus thought he’d found his match
In the still pool
But he died, lovesick, alone
For he thought he’d found his match.
--Codex Salmasianus 39