how might an argument be made that the primary system is anti-democratic

Answer 1

One way that primaries can be undemocratic is when they are "closed", meaning that only members of the political party that is holding the primary can vote in it. Closed primaries are undemocratic by virtue of the fact that they exclude participation by most citizens, but they also tend to result in the election of the most extreme candidates who can appeal to the party's base. Closed primaries could be a major reason for political polarization in the U.S.