Gal 3:10-14

In this paragraph Paul writes of the curse that attends law-breaking. Most famously Deut 28 records blessings for obedience (14 verses) and curses for disobedience (54 verses). It is all very well to claim that the gospel announces freedom from the law and the demands of the law, but we have all been disobedient to the law, what happens about the curse that follows from disobedience?

v. 10 - here Paul sets out the problem very briefly and clearly.
v. 11 - summarises much of Paul's arguments so far, the law does not make us right with God, not only because no one has fully obeyed the law, but more importantly those who are right with God (righteous) have been made righteous by faith (in Christ) not by self fulfilment of the law.
v. 12 - the contrast between the law and faith is explained in terms of work. Obedience to the law is a work, something which we do. The nature of faith is that it is a gift of God, God gives us faith and his Spirit enlivens this faith within us to our blessing.
It is like two different operating systems, works xp or faith 7, they may look as though they do the same thing(s) but they don't, and they don't function in the same way.
v. 13 - returning to the curse of the law, Paul claims that the object of faith - Christ - redeems us from the curse of the law. In his crucifixion Christ fell under the curse of the law, the reference is to Deut 21:23, one verse which stands for all the curses of the law falling upon Christ upon the cross. The key to v. 13 is the two small words 'for us'. Christ did not deserve to have the curse of the law fall upon him, he had no sin in himself. This is substitution, Christ takes our place under the curse, a place we deserve but are set free from because Christ has filled it. The curse has been borne and is fulfilled, "Payment God cannot twice demand, once at my bleeding surety's hand, and then again at mine." (Toplady).
v. 14 - and so Abraham appears again!
'so that ...' refers back to 'Christ redeemed us' (v. 13), giving the sense 'Christ has redeemed us so that ...' How would you finish this sentence? If you don't finish it the way Paul does your thinking is not yet fully in line with Paul's and the NT. So that introduces a purpose clause, the purpose of Christ's redemption of us is to bring the blessing promised to Abraham to the Gentiles!!
That all humanity were under the curse of disobedience has prevented the promised blessing being given. But now Christ has redeemed us, the curse is removed, and the blessing is freely given.
The Spirit is now poured out upon God's people through faith.

Christ removes the curse, not by force but by enduring the penalty of the curse.
To those who exercise faith in Christ and his curse removal the blessing of the promised Spirit is given.

To God be the glory.