I remember first learning this lesson from watching The Buttercream Gang. A former member of the gang goes on a rampage in the store, yelling at his friends for trying to help him. They don't understand why he is treating them so badly when they are trying to be his friends again. He answers, "Because I hate myself!" Once he learns to love himself as his friends love him, he becomes a good person again and reconnects with his old friends.
Loving ourselves is not easy. There are many reasons why we don't love ourselves: sins, weaknesses, physical insecurities, emotional insecurities, abuse, lies, false comparisons, etc. But there is one reason why we should love ourselves that crushes all the reasons not to: Heavenly Father and Jesus Christ love us. We are so full of worth that Jesus suffered agonizing pain and death for us without ever stopping loving us.
Their love is incomprehensible to our human minds sometimes, allowing Satan to plant lies about this doctrine. An article in the October Ensign addressed these lies and reminded us that God's love is unconditional and eternal and that the Atonement can take away our negative feelings about ourselves.