As humans, we love the law. Not God's law – we don't want anyone telling us what to do – but our law, laws that suit our desires. That's because we think we're good enough to meet the law's demands and on that basis, the law justifies us (me, the good person) and condemns others (them, the bad people).
Many people think that the concept of loving one another is the replacement to the law. That Christ came here to teach us to love one another, and that's what replaces the old law (that we no longer follow). Except it's not what Christ came to teach at all – Christ taught that loving one another *was* the law, and it's what the law shows us that we fail to do. The law condemns us still because we do not love God with our heart, soul and mind and we do not love our neighbour as ourselves. The requirement to love is not our salvation, it's our condemnation.
Instead Christ taught us that all of us are lawbreakers. That none of us are good. The scandal of the cross is that our sole contribution to our salvation is our sin. But the good news is that Christ died, once for all, that all who place their trust in Him can be saved – a gift that none of us deserve.
On the White Horse Inn podcast, the episode 'Good News vs. Good Advice' is excellent listening on this topic.