If something can ever err, then saying it cannot err is factually incorrect. What you are failing to do is differentiate between the Ordinary Magisterium, the Ordinary Universal Magisterium, and the Extraordinary Magisterium. The first is fallible, the latter two are not.
The magisterium is a tool. Therefore it can be infallible or not, depending. There's no contradiction whatsoever.
If you say that the sky is blue and it is, you are correct. If you say it is purple when it is blue, you are wrong. This doesn't mean that YOU are a contradiction, but that what YOU ARE SAYING is a contradiction. In the same way, the magisterium can be infallible or not, depending on what it says and how it says it.
The Ordinary magisterium is the living hierarchy, with the pope as the head. The pope can speak independently or he can teach in unison with the bishops, to use the Ordinary magisterium. If the pope is defining a doctrine, per V1's rules, it is an extraordinary teaching. We agree here.
If the pope teaches on a subject wherein he is not defining something but is re-teaching a truth which he shows as part of the universal, consistent beliefs of the Faith, then he is teaching using his Ordinary and Universal magisterium, and this is infallible because the pope is teaching and clarifying a truth using his apostolic authority. He does not need to bind anyone to believe his teaching, therefore an ex-cathedra statement is unnecessary,
because such a belief has already been defined in the past, or it is part of Tradition and has always been believed. Thus, this type of statement is to reiterate and re-teach "that which has always been taught." Example: JPII reiterated that women could never be priests and said that the matter is not open for discussion, because it is a constant belief of the faith, held since Apostolic times.
If a pope teaches on a subject wherein he is not defining something AND he is not making a clear, declaratory statement concerning a universally held belief of Faith, then he is teaching as the bishop of rome, as a private theologian and is fallible. This type of teaching does not require a blind-faith acceptance, nor does it require that a catholic believe it with a certainty of faith. Nor is a pope, when teaching as bishop of rome, immune from error, even major error, since he is teaching as a normal man, and has not engaged the protection of the Holy Ghost. Catholics must give a conditional acceptance of the teaching but to say that the pope couldn't willfully teach error in this situation, or heresy, is to deny free will.