Romans Chapter 10 Vs. 3

Israel's Unbelief

For they being ignorant of God's righteousness, and going about to establish their own righteousness, have not submitted themselves unto the righteousness of God. Rom 10:3

ignorant of God’s... This means they were ignorant both of God’s inherent righteousness revealed in the law and the rest of the Old Testament (which should have shown the Jew their own unrighteousness), and of the righteousness which comes from Him on the basis of faith.

We see from the following Scriptures, the self-righteousness of the scribes and Pharisees and how it displeased God.

Luke 18:9-14 “And he spake this parable unto certain which trusted in themselves that they were righteous, and despised others:” “Two men went up into the temple to pray; the one a Pharisee, and the other a publican.” “The Pharisee stood and prayed thus with himself, God, I thank thee, that I am not as other men [are], extortioners, unjust, adulterers, or even as this publican.” “I fast twice in the week, I give tithes of all that I possess.” “And the publican, standing afar off, would not lift up so much as [his] eyes unto heaven, but smote upon his breast, saying, God be merciful to me a sinner.” “I tell you, this man went down to his house justified [rather] than the other: for every one that exalteth himself shall be abased; and he that humbleth himself shall be exalted.”

God loves the humble in heart that are looking to Jesus Christ for their righteousness.

their own righteousness... This means their beliefs were based on their conformity to God’s law which was often the less demanding standards of their own traditions.

have not submitted... This shows their rebellion to the end.

Even though they should have known from their own Scriptures (cf. Gen. 15:6; Psm. 32:1-2). But here preferably the righteousness in view is the righteousness God requires for people to be accepted by Him, which is God’s own infinite righteousness. The Jews did not really understand God’s own infinite righteousness, which is why they were continuing to seek to establish their own (cf. Isa. 64:6). Little wonder then that they did not submit to (“place themselves under”) God’s righteousness, that is, the righteousness God provides through Christ by faith.