“[A]ll have sinned and are deprived of the glory of God.” – [Romans 3:23] We have failed God and continue to do so. So, why would God love us? He is an all-powerful and all-knowing God. He is perfect, so why does He love us who are imperfect?
Well, God calls Himself our Father. So, I believe the question is answered by looking at parents. Parents love their children. Even when their children disobey their parents, they are still loved. They may make it difficult on us parents, but we still love them so much.
“If you then, who are wicked, know how to give good gifts to your children, how much more will your heavenly Father give good things to those who ask him.” – [Matthew 7:11] We are imperfect and love imperfectly, but still love our children. God is our perfect Father and, as such, loves perfectly.
Sure, being loved does not put a burden upon us to be loved, but remember that a relationship of love takes two. If we do not hold up at least part of our side, then there is no love relationship. God still loves us and, as any parent knows, the gift of love is the greatest and yet the most painful to give. As evidenced by Jesus on the cross.