A. "This is an assertion."

B. "I'm not sure I agree with your assertion."

A. "Here is some anecdotal evidence to support my assertion."

B. "Interesting, here is some anecdotal evidence to support the opposite of your assertion."

A. "But my evidence really supports my assertion."

B. "But I just gave you an equal amount of evidence to the contrary."

The 'my anecdotal evidence is better than your anecdotal evidence' game.

It's related to experience.