We have heard it said, "Love God, Love people." But isn't it really, "Be loved by God, love God, love yourself, love people."?
"LGLP" implies a whole lot of giving back, omitting the receiving. It's because He first loved us that we love Him at all (1John 4:19). And after you have connected in the flow of His love, it is only by loving yourself that you are even equipped or able to begin to love others (Mark 12:31). If you don't love yourself, how can you expect to love anyone else?
I get where the LGLP comes from; when the scribes came up to Jesus and asked Him, "Which commandment is the most important of all?" And Jesus answered "The most important is, Hear, O Israel: The Lord our God, The Lord is one. And You shall love The Lord Your God with all Your heart and with all your soul and with all your mind and with all your strength.' The second is this: 'You shall love your neighbor as yourself.' There is no other commandment greater than these (Mark 12: 28-31)."
"As yourself" is such a huge part of it. If you hate yourself, if you are critical of yourself, or if you are unkind to yourself; how can you say that you are not so with others? You can't. Love is meant to flow through you and if that love stops at you; do you really think that it is going to flow through you untainted?
If you are in connection and dwelling with a Loving God, receiving and giving, that overflow onto others will naturally follow. How? Why? Because Love loves to love and you are a big part of that sentiment.
Just a thought...