- No A is a B
- All B are C
- No A is a C
The syllogism fails because the conclusion attempts to make a claim about all C even though the minor premise only applies to some C (all B may be C but some C may not be B). When there is a discrepancy between the scopes used in the minor premise and the conclusion the argument has an illicit minor.
In the above argument the major premise defines a relationship between Baptists and Catholics while the minor premise defines Catholics as a subset of all Christians. The conclusion then attempts to relate Baptists to the entire set of Christians instead of the Catholic subset defined in the minor premise and that makes the argument invalid.