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