Galatians 2:19 “For through the law I died to the law so that I might live for God.”
Paul now introduces the concept of "death" to the argument. He expounds on this more in Romans 7, where he uses marriage as the vehicle to explain – we are married to our spouse until they die, then we are free to re-marry. We must die to the law so that we can be free of it. The Law itself required a death, in the Temple’s sacrificial system, and the Judiazers would have focused on that concept.
“Through the law, I died to the law” Verses 17 and 18 make it clear that a person cannot himself fulfill the law – the implication here in verse 19 that trying to fulfill the law on our own strength leads to death. But once we are dead to the one concept-- like the concept of the death of a spouse as explained in Romans 7 -- we are free to live for the other “so that [we] might live for God.”