Sola Scriptura: A dialogue

In the following dialogue, C stands for Catholic and P stands for Protestant. 

C: You believe that the Bible is the inspired, inerrant, infallible word of God, right?
P: Yes. 
C: Are you infallible?
P: No.
C: Is the church you belong to infallible?
P: No.
C: Is your minister infallible?
P: No.
C: Is anyone infallible?
P: Outside of Jesus Christ, no. 
C: So, let me get this right. You believe the Bible is the infallible word of God, but that no one is infallible?
P: Yes, that's right. 
C: So, you believe that God gave us an infallible book but left no infallible person or institution that could infallibly interpret that book, so that we would be certain of what exactly God is saying to us?
P: Silence.  
C: This is the logical conclusion of your Sola Scriptura belief, that God is an idiot for leaving us an infallible book but no infallible interpreter of that book. Thus, according to that doctrine, no man could ever be certain that his interpretation of Scripture is the right one, or that his interpretation came by the Holy Spirit. Naturally, we see the logical and physical consequence of Sola Scriptura: countless denominations all equally claiming to be based on the same Bible. Are there hundreds of different ways of interpreting Scripture? If there is, then the Holy Spirit would be stupid, and that is a opinion that is offensive to Divine and Catholic Faith. On the contrary, there is indeed an infallible interpreter established by Jesus Christ to give us the true interpretation of Scripture and which can, with absolute certainty, inform us not only the mind of the human authors of Scripture, but the very Mind of God Himself of the same, and that infallible interpreter is none other than the Catholic Church. Thus, the doctrine of Sola Scriptura, whilst being anti-Scriptural, is also illogical, because it would mean that the Bible, given to men for their instruction, is unknowable and forever out of the reach of the human mind. Hence, God is made into an idiot for having left us with so precious a gift, and no one to open it for us.