You need to ask and then find the answer as to why Jesus had John take care of Mary as opposed to Jesus “UNBELEIVING biological brothers”. The answer is in how Jesus defined who was His mother, brother and sisters; which His biological and unbelieving brothers were not considered by Jesus to be His true brothers; but John was considered as one. That would later change as the biblical record shows, but at this time their conversion had not yet taken place.
Actually, St John the Evangelist was an actual relative of Christ. The point is that John Calvin himself affirmed that the Virgin Mary was a virgin throughout her life, despite the reference to the brothers and sisters of Christ.
Why would Calvin make such an “unbiblical” statement?

He also, as someone knowing Koine Greek, realized not only the tradition of the Church in this respect, but that the words for “brother and sister” could mean any number of relatives.
In the Eastern Church (which the Reformers were familiar with as well), Saint Joseph had six children by another wife who had died earlier of course. All six became disciples of Christ and the four sons became church leaders and bishops. They were, of course, “brothers and sisters of Christ” - but are NEVER called “children of the Virgin Mary.”
The deuterocanonical books of the New Testament were read widely by the early Christians in the first centuries and while they did not figure in the canon of the New Testament, the “data” they contained were never questioned as anything but true. Those books figured prominently in the liturgical feasts of the Entrance into the Temple of the Virgin Mary, for example, and for the Assumption of the Virgin on August 15 (which the Reformers kept in their calendars).
In any event, it was only in the 19th century that certain Protestants questioned this whole issue. It certainly doesn’t come from John Calvin or the other Reformers who, among other things, continued to say the Hail Mary, even liturgically (e.g. Oecolampadius - who said that a lack of veneration for the Virgin Mary is a “proximate sign of eternal damnation in a soul”).
I think any good Scriptural study would include the Christian faith milieu and ecclesial context in which the Scriptures were formed, written and codified.
I would also venture to guess that the idea that the Holy Spirit somehow became dormant in the Church after the Scriptures were canonized probably led to the 19th century views of some sects, such as the Mormonsm, the Adventists and the Jehovah’s Witnesses concerning an apostasy in the Church. The Church Fathers continued to write and teach the Scriptures and the theology it espoused for years after, and the Church herself defended orthodox doctrine in her Ecumenical and Local Councils.
That process, unbroken from the start, continues today.
Ultimately, the Scriptures were written as the core of the Apostolic tradiition within such a tradition/ecclesial milieu. It cannot be divorced from that. The view that when we read the Scriptures we will all have the same understanding of theology etc. is simply untenable and Evangelical Protestants themselves are living proof of the falseness of this perspective - something anyone, even unbelievers, can readly see for themselves.
Alex