What does Romans 11:19 mean?

Paul has warned Gentile Christians not to be arrogant about their position before God. Some might have slipped into thinking their relationship was superior to that of the Jewish people. In the previous verse, Paul wrote that Gentiles have been transplanted onto an existing root: the reality of God's relationship with Israel. That root supports them, not the other way around.

Paul imagines these arrogant Gentile Christians arguing back the words of this verse. Paul himself has said as much in his olive tree illustration. Some branches of the tree of God's people Israel have been broken off because of their refusal to receive Christ as the Messiah. That pruning left room on the trunk, as it were, for new branches to be grafted in to the root. Those branches are the Gentiles who have trusted in Christ for their salvation.

As such, Paul's imagined debaters seem to be saying, "Are we not superior to the branches that have been broken off?" Paul's response in the following verses will be that the branches had to be broken to make the new branches all the more humble about their position. After all, couldn't they be broken off, as well?