Commentators agree on two things regarding this passage: it is crucial to Paul’s argument, and it is very difficult! Part of the difficulty of this passage is that Paul has a tendency to speak in very concise, densely-structured phrases, and we are left wondering how to fill in the gaps.
To a large extent, how this section is interpreted depends on what presuppositions we bring to the text. Since the time of Martin Luther, this passage has been interpreted in very individualistic terms to mean that no one can keep the Law perfectly, and therefore justification is by faith. However, I don’t think that is Paul’s point in this passage. Let me be clear - the Bible plainly teaches that we are saved by grace and through faith, not as a result of works (Ephesians 2:8-9). There is no amount of merit any sinner can accumulate to earn God’s favor.
But that is not what Galatians 3:10-14 is about, in my opinion. The typical Lutheran approach to the passage fails in two ways. First, the Mosaic covenant was not a system based on perfect lawkeeping. The Jews very well understood that God’s election was a matter of grace (Deut. 7:6-9). Further, the Law contained provisions for dealing with human imperfection in the form of the sacrificial system. Israelites were not required to be sinlessly perfect. They could make offerings for sins and be forgiven, as Leviticus 1-6 repeatedly states.