Catholics often point out the great contradiction of Sola Scriptura (Scripture Alone). Supposedly, scripture is reliable and tradition is not, but the canon of scripture comes from tradition. The contradiction serves as powerful evidence against Protestantism and I have yet to hear a Protestant offer a convincing rebuttal to this point. However, this is not the only major contradiction within Protestant theology. The other pillar of the Reformation, Sola Fides (Faith Alone), also lacks self-referential consistency.
"Faith Alone" refers to justification, the means by which one attains salvation. Both Protestants and Catholics believe that one is saved by the grace of God but Protestants hold that sanctifying grace is given not through sacraments or any other "work" but directly from God provided that one has faith in Him. Millions of Protestants believe in the false doctrine of salvation by faith alone.
The essential contradiction of Sola Fides is that it denies the efficacy of human acts in regards to justification while simultaneously claiming that a human act is necessary for salvation. The salvic act that Protestantism endorses is faith itself. Faith is a gift from God but it is also an act of the will. When a Protestant accepts Jesus Christ as his personal savior, he is making a conscience choice to believe in something and in this way he is performing a work.* Ultimately, grace comes from God but in order to receive that grace a Christian must open himself to receive it by an act. Just as walking up to receive Communion is an act, the choice to believe in Transubstantiation is an act; it is a mental act that is expressed verbally with the word "Amen." The same principle applies to a Protestant altar call and statement of faith. Protestants don't realize it, but their theology implicitly requires a human act for salvation. Sola Fides is false.
*One might argue that this extends the concept of "works" too far, considering that the apostles made a distinction between faith and works. However, by condemning Catholic reception of the Sacraments as works, Protestants adopted a new definition of the term and it is this meaning that should be applied to Protestant theology itself.