For person X to have a meaningful relationship with person Y means, for me, that person X and person Y's relationship affects person X's life outside of just his relationship with person Y.
Lemma: if person X's entire life is taken up by his relationship with person Y, person X is incapable of having a meaningful relationship with person Y. Proof: person X has no life outside of his relationship with Y to be affected by it.
It seems that, for me, these two properties seem to be tied to one another in the following way: a relationship between me and X is meaningful only if I depend on person X. (That might be an “if and only if”—I'm not sure.) That is, if I don't depend on person X to some extent—if I don't get something from him that I can't get elsewhere—then I don't allow him to have any real effect on my life.
I'm not sure why this is, or whether it's beneficial. I'm only trying to analyze a situation, not solve a problem, at the moment.