Bad Reasons FallacyType: Formal Fallacy
Argument A for the conclusion C is unsound.
This fallacy consists in arguing that a conclusion is false because an argument given for it is bad. It is most likely to occur in the course of a debate, when one side argues badly for the truth of a proposition, and the other side uses the bad argument as a reason to conclude that the proposition is false. It is always tempting, in the heat of debate, to think that one has established one's own case when all that one has succeeded in doing is undermining the opposition's case. To commit the Bad Reasons Fallacy is to act as though argumentation is a zero-sum game in which, if the other side loses, then you win.
Since there are two ways that an argument can be unsound, there are two versions of this fallacy:
It is tempting to think that the relation between the unsoundness of an argument and the falsity of its conclusion parallels the relation between the soundness of an argument and the truth of its conclusion. The conclusion of a sound argument is always true; however, the conclusion of an unsound argument may have either truth-value. Misunderstanding this asymmetry is one psychological source of this fallacy.
In some cases, such as legal trials, where there is a presumption and a corresponding burden of proof, it is legitimate to reason that a proposition is false if all of the reasons given for it are bad. For instance, in a criminal trial in which there is a presumption of innocence, the jury should conclude that the defendant is innocent if all of the prosecution's arguments for guilt are unsound. However, it would still be fallacious to conclude that the proposition is false just because one argument for it is unsound, unless it is the only argument.
Subfallacy: Fallacy Fallacy
Nigel Warburton, Thinking from A to Z (Second Edition) (Routledge, 2001), pp. 25-26.