It’s pretty well established* that the word used here for “brethren” does not mean exclusively “the children of my mother and/or my father” but is a broader term which included near kinsmen.
There are other Biblical uses of the term when we know for certain that the referenced people have different parents.
Quite a bit of “circumstantial evidence” supports the broader translation:
Would Mary and Joseph have undertaken the journey to Jerusalem when Jesus was 12 with 6-9 younger siblings in tow? (Since the “sisters” aren’t named we don’t know how many total children Mary is supposed to have had, but if we presume that “brothers and sisters” means “immediate family” every time it appears, we have to at least account for all the named males and at least 2 females, right?)
If Jesus had four younger brothers, every one of whom would have been legally obligated to take care of their widowed mother, and probably a couple of brothers-in-law as well, why did He entrust her to His best friend when He was dying?
Why are there no mention in the extra-biblical writings of the day to siblings of the Lord? No historical or traditional references to them having lived or died in any particular location? No claims, legendary or otherwise, to artifacts or events involving someone who was a blood relative of Jesus? There is the Proto-evangelium of James, which claims to be by an child of Joseph’s by a previous wife, although the fact that it was deemed non-canonical very early casts doubt upon its authenticity. But that’s as close as you’ll get to a contemporaneous reference. Compare that with the number of stories surrounding the later lives of the Apostles . . .
Finally, it is possible to identify a number of other women as mothers of followers of Jesus with the same names as those identified as “brothers of the Lord.” It is not impossible, but stretches credulity to suggest that all these women named Miriam/Mary had all these sons with the same names:
James and John, sons of Zebedee and (Mary) Salome
James, Joses, Jude/Thaddeus, Simon and Levi/Matthew, sons of Alphaeus and Mary “wife of Clopas” (unless Cleophas is not another name for Alphaeus but another father of yet another James, this is a subject of debate among scholars)
and don’t forget John Mark the assistant of Barnabas and later Peter, whose mother’s name was also Mary (Acts 12:12)
Frankly, I don’t think we can prove Mary’s perpetual virginity from Scripture alone. I think we have to take it on faith in the authority of the Church (or not). And it is therefore not surprising that there is a huge effort on the part of people who reject that authority to “disprove” a doctrine which is, in absolute honesty, not essential to our salvation (as distinct from the Virgin Birth, which is).
(*I don’t read Aramaic, Hebrew or Greek, so am relying on the expertise of others, but it is my understanding that ancient Greek did have a different term which meant exclusively “the children of my parents.” )