I don't think any parent should attempt to arrange a romance for their child, at any age. But with young ones, kids that are not yet adults (or even some that are), a parent should discourage a romance that seems abusive: isolating, verbally abusive, or God forbid, physically abusive.
Doing so can be the most formidable challenge any parent will ever face -- anyone in such a horrible position should seek professional guidance, IMO.
Meanwhile, a child (or young adult) who shows no interest in romance may just be especially independent, introverted, etc. and unless they seem unhappy, I'd not recommend interfering.
I wonder about the marriages in cultures where the parents arrange them -- are the partners happy? Do they divorce as readily as we do, and if not, is it because women have fewer rights?
Whatever the case may be, choosing my own kid's spouse is a repugnant idea to me.