First: There are perfectly wonderful, reasonable, intelligent people who disagree with you absolutely. (And there are dunderheads who may agree with you.) The moral: judge the argument, not the person.
faulty conclusions, post hoc fallacy (cause-effect sequential but not related); non sequitur fallacy (conclusion has no connection to evidence); ad hominem argument (attach person rather than point of view);
faulty authority (when authority is in doubt); begging the question (reader expected to accept a controversial premise without proof); false analogy (two things share all characteristics if they share only a few); either-or fallacy (viewpoint can only have one of two solutions); red herring argument (deflect attention).