The Jewish part of the church in Rome were proud that they had been favoured by God: He had given His law to them.  They looked down on the Gentiles, who did not know what pleased God (Romans 2:1-4).  So, Paul brings them back to reality.  It is not enough to have received the law or even to have memorised it - if they did not obey it completely.

To be righteous, Paul said, is always to do everything God says.  That includes restraining from everything that displeases God.  Everybody who does not live in total righteousness will attract God's wrath, whether they know what is right or not.  To be declared righteous is the privilege of all those who obey the gospel (2 Thessalonians 1:8).

Paul's argument is radical.  It dismisses the fantasy thoughts that God will accept us because of our believing family, religious background or education, personal discipline, worship or charitable actions.  Because nobody can reach His holy standard, everybody is under the wrath of God (Romans 1:18). That is why we need Jesus the Saviour (1 Thessalonians 1:10).  

In a world of multiple faiths and philosophies, righteousness (by God's definition) often takes last place after 'trying my best', 'following the family tradition', 'hoping for the best', and pious devotion to religious rites.  If we cannot reach God's standard (which we cannot) our only hope is to admit our sin, repent and call out to Jesus for mercy. That applies to everybody, and especially to those who have started to trust Him. Obedience to God's Word should be our first priority; and when we fail, we must confess, repent and ask for mercy.  Living that way will please God and teach us about righteousness in a way which totally bypasses our pride.