1) We must always be careful to distinguish between arguments that are valid and those that are sound. A valid deductive argument has the proper logical structure (where true premises guarantee a true conclusion) but that is of little use if the premises themselves are false or unsure. Your expanded version of this argument is indeed valid, but the hidden premise cannot possibly be true (since human fallibility is unavoidable), so the argument is still unsound.

2) Your fallacy is the assumption that untrustworthy information is always wrong. In some ways reliably wrong information could be nearly as useful as reliably right information –it would at least enable the ruling out of some possibilities. In this case, Person A is biased therefore his information is not reliably right –but it is not reliably wrong either. Therefore, his opinion tells us nothing about the rightness of his position.

3) As we’ve discussed before, formal deductive logic is an artificial system designed to extend and improve upon (and theoretically to perfect) the conclusions reached by raw human intuitions (while inductive logic might perhaps be described as the mid-ground between the two). The tendency to confuse the rules of logic with the intuitions that inspired them does indeed have psychological and sociological aspects –but the same could be said for nearly all human practices.