St. Mark tells us the names of for of the "brothers" of Jesus -- James, Joses, Judas, and Simon. The term "brother" is often used in Scripture to refer to a cousin rather than to a literal blood brother.
We know that these cannot be blood brothers of Jesus, son's of Mary and Joseph. Indeed, St. Matthew (27:56) specifies that the mother of James and Joses was another Mary who, St John (19:25) tells us, is the wife of Cleophas! The Catholic Church knows the Bible better than any protestant, because Catholics were the ones who wrote the New Testament.
These "brothers" aren't children of Mary, nor are they children of Joseph from a previous marriage -- Matthew 27 and John 19 show that they are the children of Cleophas and another Mary not Mary the Mother of God! Nothing in Sacred Scripture would lead us to think that Mary had any children beside Jesus, nor even that St Joseph had any children from a previous marriage; in face, the Bible teaches that the "brothers and sisters" of Jesus can't possibly be children of either Mary or Joseph.
We consider further that the people of Nazareth rejected Jesus precisely because they didn't pay due honor to Mary and Joseph and the other saints -- if we want to be true followers of the Lord, we must be intensely devoted to those two to whom He was most devoted, Mary and St. Joseph. Further, we must beg our Savior for a true love and reverence for all the saints.
Listen online [here]!