To be clear, I meant that the conversation (the argument) would be a better experience for everyone involved, not the argument itself being somehow strengthened by it.
Nevertheless, I'll try to recall how I arrived at this conclusion. The biggest influence was seeing for all my life, the left and right in America each claim the other is stupid, irrational, and un-convinceable by rational argument. When I was 16 it really did seem to me that the right was the irrational side here, but seeing everything come full circle with what's happening on the left these days, I realized it's kind of weird and unlikely that half the population, divided on a political line, is actually worse at thinking than the other half.
(See the bottom of this thread for a vivid example.)