But here is a point the lawyer seems to be missing. In American courts, the law of the land is the Constitution. All "friends of the court", i.e. attorneys, prosecutors etc. are required to pledge allegiance to the flag because it represents the nation, and its laws. By refusing to pledge, a judge can assume you have no allegiance to America, and therefore no allegiance to its laws. If you have no allegiance to America or its laws, you have no right to be practicing law in American courts.
And while the attorney certainly does have a right to remain silent, the judge also has the right to deem that to be contempt of court.