When someone cares for your child they are embracing you too because you are expressed in your child. If someone likes you but not your child, that is a contradiction to you. So too with G-d for we are each a child of G-d (Deut. Devarim 14). To love G-d but not the other is a rejection of G-d because each person expresses G-dliness in a unique fashion, a child of G-d. This includes the imperative to love ourselves too.
Mendel (Menachem) Bluming paraphrased from Hayom Yom