Not true. I don't love myself, I don't value myself, mostly I don't respect myself either. Still, my girlfriend loves the literal fuck out of me. My family loves me regardless of whether I love myself or not. This "if you don't love yourself, then how will you ever love someone else" is bullshit. Love isn't something static or based on logic. Sometimes it's just there. These are just worthless platitudes or cliché's that actually help nobody.

Respect and value are other things, however. If I don't respect myself, I might let someone be rude to me. Walk all over me. If I respect myself I will stop it before it happens and they will learn that I do not tolerate that. Same with value. If I don't value myself a girl may just cancel dates with me and I will just sit around and wait for her and that will cause her to not value me. If I value myself I will simply walk away and she will realize that I value myself more than to just wait around for her.