The law was insufficient for salvation because humanity isn't formed to be perfect. God seeks reconciliation where man seeks judgement. That's why the law cannot bring salvation. Jesus fulfilled the law because the commandments on His heart were only 2:
-Love the Lord your God with all your heart, mind, and soul.
-Love each other as you Love yourself.
It takes great depth of understanding of human nature to learn to Love with fullness, and the Love needed to save humanity can only come through the acknowledgement of great suffering we cause one another. That suffering is what separates us from knowing God's love for us. This is what agape means.