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> but it was given to a people who constantly sinned, even when trying to display faith

Where do you even get that from? It wasn't given to people before the flood whose imaginations were constantly evil. If you sinned just a bit you still were obliged to keep the whole Law back in Israel, you weren't released from it. 
> This is why it wasn't given to Noah or Abraham right away, since they were righteous men.

All have sinned. All have come short. None is righteous, not even one. Justified is somewhat different than righteous.
> Out of context.

You've failed to explain how is it out of context. You are attacking an argument that Levitical Law is sinful which has not been made.
> This is what Jesus is correcting, the Pharisaic interpretation. 

This is what's written in the Law. He's not correcting rabbinical teachings that were not found in Torah. He is correcting Mosaic Law. He is giving wildly different interpretations than what is meant - spirit of the Law. He outright stops legally required judgement on an adulterous woman. There's no allowance for that in the Law. Love thy neighbour, but hate thy enemy, that is the Law and it is blatant contradiction of Jesus' teachings.
> How have we "died to flesh"? We are still flesh, and we are still sinners, all of us. 

Things like this make me wonder if you've read the whole New Testament or just went through verses here and there that justified 'judaizer' position in some theological thesis. 
Galatians 2:20, Galatians 5:24 and there is more like Romans 6:11-12 but you might want to argue that death to sin is something different. Babtism is ritual death and rebirth also. By accepting Christ you legally die. 
You were justified in Jesus Christ. Not justified so you can go back to doing the Law, there were ways to remove your transgressions in the Law already. The Law has been fulfilled. You cannot fulfill it any more than it already is.
> but it IS a way to live

You are running in circles. The Levitical Law appeared only in a certain nation in a certain period of time. If the Law is a way to live God made it impossible for everyone before it had appeared to live a life acceptable to Him but we know that in every nation he who is fearing Him, and is working righteousness, is acceptable to Him and we know that Abraham was justified by Faith. Not the one who does the Law! You cannot do the Law without the temple so 'righteousness' cannot mean 'works of the Law'. Not 'a temple' THE temple, the building in Jerusalem. The Law is not required by God of you and even if you were to keep every precept of the Law it is not sufficient for God or Jesus would not have redefined it in so many instances.
> Because following the Law isn't what traps you.

Oh it does. 
Cursed is every one who is not remaining in all things that have been written in the Book of the Law -- to do them. Jesus Christ did it all perfectly so you don't have to and you're saying 'thanks, now I'll do it myself'. You are given the most beautiful mansion by your Father, one you could never afford, and rather than live in it you try to build a shed of your own saying say "since I have a place to lie down I can build my own house". This is not what it appears to you as but this is what you're doing if not outright rejecting Jesus.