Belief bias
Belief bias is when we judge the strength of an argument by how believable its conclusion is, rather than by whether it logically follows from its premises. A conclusion we agree with is accepted more easily; one we dislike is scrutinized more. So we can accept bad logic when we like the conclusion and reject good logic when we don't. Related: Begging the question (evaluating by conclusion rather than form).
Examples
We rate "All birds have wings. Eagles are birds. So eagles have wings." as a strong argument, but the same logical form with an unbelievable conclusion—"All birds are yellow. Eagles are birds. So eagles are yellow."—as weak, even though both are valid. We're swayed by how believable the conclusion is.
An argument that leads to a conclusion you find unpleasant is dismissed as flawed, while a similar argument leading to a conclusion you prefer is accepted without the same scrutiny.
In a jury, a verdict that "feels right" is adopted even when the logical steps from the evidence are weak.