We’ll start with these. They may be “easily” shot down, but I’ve never seen them “effectively” shot down.
Mary as “Mediatrix”
Immaculate conception
Perpetual virginity of Mary
For anyone who might happen to come across my previous post, that is a list of examples where Catholic tradition contradicts scripture. (I’m not defending the doctrines. I’m saying that the statement that they contradict scripture has not been effectively refuted.)
I’ll start with perpetual virginity.
First, close kinsmen were often referred to as brothers. James the Just, the Brother of the Lord, has sometimes been identified with one of the apostles named James, James the son of Alphaeus (who apparently was also called Clopas, perhaps as a family name or resulting from the different languages and titles in the now multicultural Israel of Jesus’s time) whose wife was also named Mary and who was related to Mary, the Mother of Jesus. This Mary of Clopas was also present in Jerusalem during the Passion of Christ, 1 of 3 women named Mary (along with Magdalene and Jesus’s mother) who were mentioned in the Gospel accounts. This Mary is also seemingly identified as the mother of Joses and Salome, who were also identified as Jesus’s brothers.
Also, if Mary,Jesus’s mother, had other children, why would Jesus entrust her to John the Apostle before His death?
I am no expert on Mary, but the arguments put forth at least make some sense.
Some other traditions (and these can be found in some early non-canonical writings), dating back to early Christianity, make some of the people identified as “brothers of the Lord”, as children of Joseph, who was a widower before he wed Mary after the Annunciation.