After discussing how God does justice fairly to both Jews and Gentiles (non-Jews), Paul focuses on the Jews. The Jews not only have familiarity with the Law and God but also approve of the Law and God, and they have a calling to be a guide and teacher (2:17-20). But nevertheless, like the Gentiles, the Jews still have done sin and would still fall short of God's standards.
For a demonstration of point, Paul rhetorically asks if those "who teach another [...] not teach [themselves]" (2:21). Examples include stealing, doing adultery, idolatry (via robbing temples), and the overall breaking of the law (2:22-23). Although the Jews teach others to not do these things, they still do some of the things -- some of which are really bad actions! Thus, Paul talked about how those who "make [their] boast in the law [...] dishonor God through breaking the law" (2:23).
Making a boast in the law while not following the law can be a big problem. Paul even talked about how "the name of God is blasphemed among the Gentiles because of [the Jews]" (2:24). This is one of the big effects of religious hypocrisy, and even today, religious hypocrisy is a BIG problem in the church.