I find this an interesting thing to think about. I'm not known for loving myself yet I don't (currently) hate myself either.
My situation is that I was married for almost 9 years and as soon as that ended I immediately started dating someone (that was 7 months ago) so I haven't been "alone" in over 10 years. I'm not in love with the man I'm dating but we care about each other.
That being said, I agree, it's easier to love yourself or at least care more positively for yourself when there is someone else there giving you that kind of positive feedback. It's just a reassuring thing. I'm pretty certain that if/when this relationship ends it's going to spiral me down very fast. I am afraid I'll go into a very dark place and I have a feeling at that point I will possibly hate myself, but if I'm lucky I'll just dislike myself.
How do I pull myself up when I don't have someone else to show me my good side or at least validate that I have positive attributes? When I am in a dark hole full of despair and sadness how am I supposed to be able to dig up things to love about myself? It's hard enough to survive the days, how am I supposed to find a way to love myself?
So no, I don't think someone else loving you equates to you loving yourself but I totally get what you're saying and I just hope you know that you're not alone and you are cared about - at least by many people on this site