They don't. I have little to no self-esteem and I'm in a relationship. And even though I struggle to love myself at all, I love him very much. It's a lie that you can't love someone without loving yourself first. In fact, there may be more truth to the opposite: if someone shows you love (not necessarily just within a romantic relationship, you would HOPE that that would come from your parents), then you learn that you are worthy of love and you can learn to love yourself.

These sorts of phrases keep people with low self-esteem DOWN. I don't know how they help at all. I guess people with high self-esteem don't understand that telling someone with low self-esteem that they can't have something they desperately need because of their low self-esteem will just make them beat themselves up further.