What does the quote the thing you hate about an argument is that it always interrupts a discussion mean?

This answer has no defacto or absolute integrity since it innately invites you to give your own opinion. So in that respect, my answer would be as follows;

"Having a discussion leads to productive comments such as ideas to solve a problem scenario. Arguments are simply a barrier that prevent you from extracting any such useful dialogue, since you're always rebutting the adversarial remarks to ensure you have the last Word.