Non-Catholics bristle at this notion, as I once did too, and insist that each one of us has the ability to interpret Scripture for themselves based on their membership in the body of Christ. The problem that arises is when private interpretation of Scripture leads to divergent and oftentimes opposing views. Ultimately divisions and branches are formed when each party holds to their own particular interpretation of Scripture. I struggle with the notion of "private interpretation" because it implies that Jesus, who gave us the Holy Spirit to guide us in all Truth, is allowing certain bits of Truth to be "up for grabs." These areas of divergent opinion are sometimes termed the "non-essentials" but often they are about salvation/eternal security/meaning of Baptism, and are indeed very essential truths.
In my discussion with brethren who hold to the idea of Sola Scriptura (That all truth must be contained in the Bible alone), they insist we need no magisterium to tell us what to believe because the Bible doesn't mention it explicitly. They say that their own interpretation of Scripture is the correct one since "it comes directly from the Word of God" and they just let "scripture interpret scripture." I wish it was that easy! Even Luther at some point bemoaned "private interpretation" when he said "Every man that has a head has become his own pope!"
(Refer to my earlier post regarding Sola Scriptura here)
I submit that "NO MAN IS AN ISLAND" particularly when it comes to developing a theology /belief system and in actuality, every man does subscribe and submit to his own "magisterium." You do and I do. It may be the magisterium of their favorite pastor or bible teacher, or the magisterium of their personal friends who they are in agreement with regarding areas of faith and morals. It could be the magisterium of "Radio Bible Class" or it can be the Chinese Restaurant Magisterium (I'll take one of those from Column A and two of those from Column B) Which is what I did for many years! In other words, none of us, if we are completely honest, study the Bible with a totally blank and open mind (skull full of mush so to speak) and let the Holy Spirit give us the correct interpretation of Scripture. We rely on our past religious education, denominational affiliations, memories, and moral inclinations and experiences. It would be impossible to do otherwise.
Catholics and Non- Catholics both have a magisterium. It's just that we believe our Magisterium is the teaching authority Christ entrusted to his apostles when he established the Church on Peter. We believe this has continued in apostolic succession through the ages even despite some popes who were real scoundrels. However, when it came to issues of faith and morals, even the stinkers didn't pervert or twist truth. That was the Holy Spirit's divine protection and the "charism of infallibility."
Jesus did not leave us alone, but in his kindness and mercy left us with the Paraclete who will lead us in all truth. Catholics believe this process occurs via the Magisterium of the Church. The way I see it, the things our Lord wants us to know about Him are too precious to be left to chance and our own admittedly fallible private interpretation. So Jesus gave us His Church through which the Holy Spirit continues to guide us infallibly through fallible men. We believe scripture supports this view in Timothy, when Paul tells the people that the household of God, the Church, is the pillar and foundation of truth. (II Timothy 3:16)
This is what the Catechism says about it:
"The task of giving an authentic interpretation of the Word of God, whether in its written form or in the form of Tradition, has been entrusted to the living, teaching office of the Church alone. Its authority in this matter is exercised in the name of Jesus Christ. This means that the task of interpretation has been entrusted to the bishops in communion with the successor of Peter, the Bishop of Rome."
CCC 86 "YET THIS MAGISTERIUM IS NOT SUPERIOR TO THE WORD OF GOD, BUT IS ITS SERVANT. It teaches only what has been handed on to it. At the divine command and with the help of the Holy Spirit, it listens to this devotedly, guards it with dedication, and expounds it faithfully. All that it proposes for belief as being divinely revealed is drawn from this single deposit of faith."
CCC 890 "The mission of the Magisterium is linked to the definitive nature of the covenant established by God with his people in Christ. IT IS THIS MAGISTERIUM'S TASK TO PRESERVE GOD'S PEOPLE FROM DEVIATIONS AND DEFECTIONS AND TO GUARANTEE THEM THE OBJECTIVE POSSIBILITY OF PROFESSING THE TRUE FAITH WITHOUT ERROR. Thus, the pastoral duty of the Magisterium is aimed at seeing to it that the People of God abides in the truth that liberates. To fulfill this service, Christ endowed the Church's shepherds with the charism of infallibility in matters of faith and morals. The exercise of this charism has several forms."