We are required to believe in Mary’s perpetual virginity, meaning that she was always a virgin and had no other children, and that Jesus’ birth was a miraculous one, not in any particular hypothesis accounting for the exact nature of the relationship of these persons called Jesus’ “brothers” in Scripture, according to standard Hebrew/Aramaic cultural custom.

Some believe that these “brothers” were Jesus’ cousins; others, that they were step-brothers, and sons of a previous marriage of St. Joseph. Linguistics alone do not at all require the interpretation of “siblings.” Nor do cultural understandings of the ancient Hebrew family, as I shall presently explore. 

Here is a description from a website called Ancient Hebrew Research Center. It is referring more so to the nomadic, Old Testament period, but I suspect that in Jesus’ day it wasn’t all that different:

The family, children, parents and grandparents, all resided in one tent. The clan consisted of the extended family, grandparents, aunts, uncles, cousins, etc., all residing in one camp and may contain as many as 50 to 100 tents laid out in a circular pattern. When the clan becomes too large for one area to support, the tribe splits into two clans (see Genesis 13). All the clans (all being descended from one ancestor) may cover hundreds of square miles making up the tribe. As an example, the house of Moses, of the clan of Levi, of the tribe of Israel.

The Hebrew “household” (if not virtually always) often would contain extended family members. It was not like our nuclear families of today. For example, in the book, Families in Ancient Israel (Leo G. Perdue, editor; Westminster John Knox Press, 1997) we find this description:

The familial roles of males in the household’s kinship structure included those of lineal descent and marriage — grandfather, father, son, and husband — and those lateral relationships — brother, uncle, nephew, and cousin. (pp. 179-180)

The household often even extended to sojourners or hired laborers (ibid., p. 199). In this book, the “household” is casually described as including cousins. For example:

The line of responsibility to serve as the household’s or clan’s “goel” began with the brother, then the uncle, then the cousin, and, finally, any close relative. (p. 192; goel = “redeemer,” or the one “responsible for the justice and well-being of the family”)

The Eerdmans Bible Dictionary (edited by Allen C. Myers, Grand Rapids, Michigan: Eerdmans, rev. ed., 1975) makes the nature of the Israelite family very clear, by noting that it could include more than one nuclear family (thus, cousins would be residing together):

The basic social unit, comprised of persons related by kinship and sharing a common residence. The Israelite family was an extended family known as the “father’s house” or “household” (Heb. “bet-ab”), consisting of two or more nuclear families (i.e., a married couple and their children) or composite families (an individual with multiple spouses and their offspring) . . . other kin (including grandparents), servants, concubines, and sojourners might also be reckoned part of the household (cf. Gen. 46:5-7, 26). (“Family,” p. 376)

Moreover, on the next page, this reference work noted that clans also usually “occupied the same or adjacent towns.” Extended families stuck together. It was like a perpetual family reunion. This would account for first or second or third cousins (all referred to as “brothers” in Semitic or Near Eastern culture: then and now) “hanging around” in one place.

To conclude: François Rossier, in his article, “The ‘Brothers and Sisters’ of Jesus: Anything New?” notes how the New Testament use of “brothers” when meaning “cousins” is explained by analogy:

[A]ncient Hebrew . . ., like Aramaic, does not distinguish between blood brother and cousin. In fact–and this point might not have been taken into sufficient consideration–the Hebrew word “ah,” in its literal meaning, applies to any close male relative of the same generation. Once someone belongs to this circle–whether as sibling, half-brother, step-brother or cousin–he is an “ah.” Within this circle defined by true family brotherhood no further word distinction is made. For ancient Hebrew, one belongs either to the family in-group or not. . .

The psychological and anthropological reality of speaking and writing in a language of another culture is, however, more complex. I was able to witness it when I was living in Abidjan, the major city of the Ivory Coast, in West Africa. It is today a big city of about 4 million inhabitants that grew up in a zone originally scarcely populated. The sparse original population was not able to absorb the waves of immigrants coming from all over the former French colonies in West Africa. The only language all these people had in common was French, and French became thus the native language of Abidjan. In most native languages of West Africa, no distinction is made between a “brother” and a “cousin,” whereas such a distinction exists in French. Nevertheless, the inhabitants of Abidjan, whose mother tongue is French, who have been raised and educated in French, continue to use the French word for “brother” when they speak of a “cousin.” . . . When the people of Abidjan want to specify that “brother” means a true blood sibling, they need to add “same father, same mother” (“même père, même mère”). Full siblings are a particular kind of brothers; they do not constitute the benchmark of brotherhood. The socio-cultural milieu of the authors of the New Testament is Judaism. So, we can accept the idea that, even if their text does not suppose a Hebrew or Aramaic substrate, in their use of Greek words they would naturally convey the way their own Judaic society and culture envision social and family relationships. . . .

Nowhere in the New Testament are the “brothers” of Jesus also identified as “sons of Mary” within the same context. Whereas, again in Mark 6:3, Jesus is identified as “the son of Mary” by the people of Nazareth.