Actually, the "eye for eye, tooth for tooth" from Torah is interpreted the opposite by Jews as it is by Christians, which as a Jew is very odd to me.
Christians tend to see it as a "compensation" law, a "retaliation" permission system, or worse--a law permitting capital punishment such as the death penalty.
Jewish law is designed with a complexity often poo-pooed by Christians, as if the Jews don't know what they were writing about when we wrote it and that Gentile Christians, foreign to our culture and language know far better.
This law, in combination with others, has led Israel to outlaw capital punishment, retaliation, revenge, etc. Through the study of Torah, Jews have learned as it is written in the Mishnah: "Whoever destroys a soul, it is considered as if he destroyed an entire world." --Mishnah Sanhedrin 4:5.
As for that Psalm in Hebrew, it reads:
"So inherently sinful I am, that with sin my mother brought me fourth."
The psalmist was not saying he was born "in sin" as Judaism does not hold to the view of Christianity and it's Original Sin doctrine. Instead he was poetically speaking of how deeply he felt guilty of sin. So great it was that he felt it was inherent, as if his mother conceived him not in a womb but in sin itself.
The term "with" can mean "in" but in English that makes people think of Original Sin instead of sin being a stand-in for the womb as it does in the Hebrew.
You are all reading it wrong, as if the Jewish composer was a Christian who accepted the Catholic teaching of Original Sin. It is "in sin my mother conceived me" as opposed to "in the womb my mother conceived me."