[metmom]

To explain the reason for the good works, that we might walk in them.

Doing good works brings God honor and glory and testifies to the validity of our faith. They do not save us. Works don’t save because they can’t save.

Without the shedding of blood, there is no forgiveness of sin. There is no other means of salvation.

[annalex]

Doing good works brings God honor and glory and testifies to the validity of our faith. They do not save us

So god repeatedly urges us to bring him glory even though it has nothing to do with our salvation. Why can't God bring Himself glory? How is it that our works cannot save us, but can glorify omnipotent God?

Without the shedding of blood, there is no forgiveness of sin

That is a different argument. The Catholic teaching agrees with this: without the Sacrifice of the Cross there is no salvation. Let's remember this when you ask why crucifixes show the Sacrifice of the Cross.