The first, a conditional argument, I have paraphrased as follows (all material from Whitaker in this post can be found on pages 332-334):
If Scripture was divinely authoritative before the Church declared it to be so (e.g. at a local or ecumenical council),
Then Scripture has an intrinsic authority over us that does not depend upon the decrees of the Church.
Whitaker thinks the antecedent "is manifest" and I see no reason to disagree. I am not aware of any Catholic apologists who argue that the Magisterium made Scripture authoritative and inspired; they instead seem to argue that Scripture is inspired by God, but the recognition of it being inspired comes through the Magisterium. For example, Madrid asserts that:
The Church did not make those books [of Scripture] inspired; God did. Similarly, the Catholic Church did not make them 'canonical'; God did, by the very fact that He revealed them.1
As for the consequent, Whitaker gives four supporting reasons. I've decided to limit this post to the second and fourth reasons, which I found to be the most reasonable and least confusing.
Here is the first of the pair:
The judgment of fathers, councils, and the church, is but recent, if we respect the antiquity of scripture. If therefore the authority of scripture depend upon the public judgment of the church, then doubtless for many centuries there was no certain canon of scripture. Fathers, indeed, and councils enunciate the canonical books; but those books both were, and were esteemed, previously authentic, and canonical, and sacred, as is plain from those fathers and councils themselves. Let them produce any public judgment of the church, and it will readily appear that the scriptures were deemed canonical before that judgment.
i) Someone might object that the lists given by church fathers and local councils were not the same as the canon we have today. That is true in some respects, but in general we are dealing with a few books difference here and a few books difference there. That is rather difficult to reconcile with the Catholic claim that we need the Magisterium to recognize the canon at all, that without it we wouldn't be able to know any of the books of the canon. (I have heard some arguments to this effect which challenge Protestants to sort through all of the ancient literature available during the Apostolic age and decide what is and isn't the Word of God.)
ii) This is also functions as a useful historical observation. The early church did not approach the canon as something that could only be truly known through the decrees of councils. This is yet another disconnect between the modern Roman Catholic denomination and the early church.
And here is the second (emphasis mine):
If the church be gathered together to consign the canon of scripture, it must needs be so by some authority. I demand, therefore, by what authority it is so collected? If they answer, by some internal impulse or revelation of the Spirit, we entirely reject such revelations which are besides the word, as fanatical and anabaptistical and utterly heretical. If they say that it is collected by the authority of scripture, then they concede that which we demand: for it will thence follow, that the scripture had a canonical authority before it was confirmed by the judgment of the church. If they allow only this part of scripture which gives such an authority to the church to have been previously canonical, but deny the rest to have been so, they do this without any certain reason.
This is an interesting dilemma, and I'm not sure if there's a way out for the Roman Catholic. It seems rather powerful.
I do know that modern Roman Catholics tend to take the latter option and argue for the authority of the Magisterium from Scripture (e.g. arguments from Matthew 16:18). But the epistemic dilemma Whitaker is driving at cannot be avoided. If I, as a Protestant, need the Magisterium to know that Scripture is authoritative and binding, of what use is it to quote Scripture to me in order to prove the authority of the Roman Catholic denomination? If I take the Roman Catholic assertion on this point seriously, then I am in no place to rely on Scripture to prove any doctrine or position, let alone that the Magisterium has the authority to identify Scripture.
In other words, if Catholics want to use Scripture to prove the authority of the Magisterium to Protestants, they admit that it is already binding on the consciences of Protestants before they come to believe that the Magisterium is authoritative. But if Scripture is already binding before it is known that the Magisterium is authoritative, why do we need the Magisterium to show us what is and isn't Scripture?
1. Patrick Madrid, Answer Me This (Huntington, IN: Our Sunday Visitor Publishing Division, 2003), 128.