Generally romantic love involves eroticism or actual sex.

Exactly the response I was fishing for.

To that I respond, asexual people still have relationships, people who can no longer engage in sex have romantic partners whether that be from injury or deterioration of bodily functions.

If the people in groups which either don't experience sexual attraction, or cannot engage in any sexual acts can be in a romantic relationship, what then is the differentiating characteristic?

asexual people still have relationships, people who can no longer engage in sex have romantic partners whether that be from injury or deterioration of bodily functions. — CallMeDirac

As I said an erotic component OR sex. You don't need to engage in sex to have an erotic/romantic relationship with someone. If the relationship is asexual then it is platonic. Anyway that's my view. The subject may be infinitely richer than this.

To clarify I am using platonic to mean friendly, a platonic love is a friendly love, that which one would find between friends.

By your definition, unless someone was sexually attracted to their partner they cannot have a romantic relationship, yet asexual people can and do have romantic relationships.

By your definition, unless someone was sexually attracted to their partner they cannot have a romantic relationship, yet asexual people can and do have romantic relationships. — CallMeDirac

I'll take your word for it.

To begin with, I discern that "the difference" between lovers and friends is the latter seek to enjoy mutual independency and the former seek the passions of mutual dependency ...

yet asexual people can and do have romantic relationships — CallMeDirac

How is it so? Is it a kind of intimacy that doesn't imply sexual arousal?

As a society, we acknowledge a difference in romantic relationships and friendships, but what is that difference? I have concluded it is entirely a socialized difference, I am looking for arguments against that conclusion.

Intimacy doesn't necessitate arousal, people will spend time with their partners without the intent of sex nor a feeling of sexual arousal. Thus, there must be something about romantic relationships that doesn't have to do with sex that is distinct from friendship.

Thus, there must be something about romantic relationships that doesn't have to do with sex that is distinct from friendship. — CallMeDirac

True. That must be love. Intuitively, there is a big difference between friendship and love. Are you suggesting that there is no such difference?