^There's no correct answer with abstraction.
I suppose that's right, but in this case I think it's as close to correct as is possible.
For instance, does a mum who doesn't love herself, automatically not love her child?
Does a once-attractive woman who has been disfigured and now feels complete self-loathing, no longer love her husband?
It's highly unlikely that a person who does not love themselves is less capable of love than a person who does love themselves, and to such an extent, that the person who does not love themselves cannot love another person.