Dead works are based on the fact that for EVERY.OTHER.RELIGION. you need to save yourself - from Sanatana Dharma: Hinduism/Buddhism/Jainism you have to escape the cycle and build your own karma. Similarly Zoroastrianism is about being good, Judaism / Islam is about following the rules.
Christianity is a revolution in that case --
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yet we have Wherefore, my dearly beloved, (as you have always obeyed, not as in my presence only, but much more now in my absence,) with fear and trembling work out your salvation which means to me that we can't save ourselves in line with For it is God who worketh in you, both to will and to accomplish, according to his good will. -- so the "being good" is in itself God working in us
I consider dead works to be a subset of sin because they are sin. Unlike man, God knows motive. And they are missing the mark, which makes them sin.
However, I’m trying to explain, in a few sentences, something that could be explained in a few books. ;)