Person A makes claim X.
Person B makes an attack on A's circumstances.
Therefore X is false.
A Circumstantial ad Hominem is a fallacy because a person's interests and circumstances have no bearing on the truth or falsity of the claim being made. While a person's interests will provide them with motives to support certain claims, the claims stand or fall on their own. It is also the case that a person's circumstances (religion, political affiliation, etc.) do not affect the truth or falsity of the claim. This is made quite clear by the following example: "Bill claims that 1+1=2. But he is a Republican, so his claim is false."
There are times when it is prudent to suspicious of a person's claims, such
as when it is evident that the claims are being biased by the person's
interests. For example, if a tobacco company representative claims that tobacco
does not cause cancer, it would be prudent to not simply accept the claim. This
is because the person has a motivation to make the claim, whether it is true or
not. However, the mere fact that the person has a motivation to make the claim
does not make it false. For example, suppose a parent tells her son that
sticking a fork in a light socket would be dangerous. Simply because she has a
motivation to say this obviously does not make her claim false.
"She asserts that we need more military spending, but that is false, since she is only saying it because she is a Republican.""I think that we should reject what Father Jones has to say about the ethical issues of abortion because he is a Catholic priest. After all, Father Jones is required to hold such views." "Of course the Senator from Maine opposes a reduction in naval spending. After all, Bath Ironworks, which produces warships, is in Maine." "Bill claims that tax breaks for corporations increases development. Of course, Bill is the CEO of a corporation."