A law draws a line; inside the line is right and outside the line is wrong. The law goes one step further for enforcement — there is a penalty if you go outside the line. The power of law is the fear of punishment. The assumption of law is that you want to go outside the line but fear will rein you in.
Scripture tells us that when it comes to sin, law only helps us to know where the line is but is powerless to keep us in line; only burdening us with guilt and fear. Furthermore, Scripture tells us that righteousness is not merely keeping within the line but calls for us to move inwards, towards the centre. Righteousness is not that we do not kill our neighbour, but that we act out of love towards him. Law cannot do that.
But Law is attractive because it “justifies” us. We can pretend we are righteous because we have kept ourselves externally within the Law while in truth, as Jesus points out, in our heart we would have gone far beyond all lines.
Law is attractive also because it allows us to differentiate ourselves: we are better than them. In doing so we go a step further in our false sense of righteousness: we are righteous because they are so sinful.
Finally, Law is attractive because being clearly defined, it can be manipulated. If I do this or that, then this is lawful. If the circumstances are such, then I am alright to indulge in this way. Even more, there will be interpreters of the Law, able to bend the Law this way or that way.
There is nothing wrong with the Law. But it cannot solve the problem of sin.
Grace places the problem of sin on a different playing field. It sets aside the Law and its system of punishments and instead brings in the Holy Spirit to be the One who will teach us righteousness and empower us to overcome the pull of sin to step beyond the line, and instead enlists the power of Love to draw us inwards to the heart of God. The goal of Grace is the same as Law: righteousness. But the methodology is radically different.