To argue that the process is not democratic, you simply need to point out that the judges are not elected. Electing people is the most democratic way of selecting them.
To argue that it is democratic, two points can be made:
- We are represented in the selection process. We vote for the president who nominates the judges and we vote for the Senators who vote on whether to confirm the nominees. Therefore, we have a say in the process.
- This selection process protects democracy. Majority rule is not all of democracy. Democracy also involves protecting the rights of unpopular minorities (whether they be racial, political, religious, or any other type of minority). The indirect selection process we have makes it more likely that judges will not give in to the whims of the majority and abuse the rights of minorities.