The phrase is worthless the way it's used 99% of the time, to preserve the notion that the world is fair, that people who are well off earned it through their own goodness and to easily shift to blame to the victims cuz the thing is what the people throwing that around miss is that you need to receive love, to feel accepted and belonging to love yourself in the first place and likewise self hatred is born from shitty circumstances and from the rejection and devaluing from society and other people to yourself.
And as for why I love myself? I don't, I have hated myself for plenty of years now but I try to be kind to myself when my mental state allows me to as at the end of the day just because I am stuck in my body I try to minimize my suffering and that is not achieved through negativity but self compassion, understanding and actions that allign with those things.
And I was only able to find some of that so called self love when I understood that the reason I am suck a fuck up is largely due to the abuse, terrible parents, isolation from my neurodivergence, society's values to which I did not measure up to and other such circumstances I had growing up.
For instance, and sorry if this is uncalled for, but I can relate a bit to you which incites me to chime in and I read you saying elsewhere that you see no point in doing anything about your health or body, however I'd think that by mere fact that you are a decent person and have feelings nor did you ask to be born, you deserve better than the suffering you go through and hence it makes sense to seek ways to ease your suffering as long as you remain in this world which a better health might help with, but I know how empty it feels to hear any of this from anyone else so I don't presume to push you to do anything.
Lastly for how I believe self love relates to relationships with others I can confidently say you don't need to love yourself for others to love you, this can be seen all the time with people who are all kinds of fucked yet loved all the same, but self love is certainly good to have to build healthy relationships. Not that I have any of those lol! But I have ruined some relationships with people due to my insecurity and other such related issues so I can at least say what does not help.