Remember what has gone on before. It is dishonest to ignore the context of prior exchanges. Remember what both your partner and you have said. Memory is brief only in verbal argument, written copies can show you to be forgetful. If you don't want to be consistent, it's OK as long as it's above board.
Broad claims tend to be very weak.
There may be counter examples, better alternative explanations, or just plain little support beyond coincidence. Frequently, broad claims arise in propaganda or rhetoric rather than in careful analysis. Be suspicious of such claims, and treat them more as hypotheses than facts. Admit when you've been wrong. You'll be admired for your honesty, and will then have a point of agreement as a basis for further discussions.