Why Mary is called the Ark of the New Covenant
Read Luke 1 along with 2 Samuel 6. You'll find at least 4 parallels or prefigurements which led some Church Fathers to give Mary the title of Ark of the New Covenant.
1. David said, "How can the ark of the Lord come to me?"
Elizabeth said, "How has it happened, that the mother of my Lord would come to me?"
2. 3 months in similar hill country: 2Sam6:9-11 David rerouted the ark to not come immediately to the city of David. "The ark of the LORD remained in the house of Obed-Edom the Gittite for three months, "
I don't know ancient Israel geography well enough, but I've read that this is the same area as mentioned in Luke 1:39 "At that time Mary got ready and hurried to a town in the hill country of Judea, " where she stayed for 3 months.
3. The word for glory or power in Luke 1:35 "The Holy Spirit will come upon you, and the power of the Most High will overshadow you." is translated from the word "shekinah" (the the glory cloud) which signified God's presence associated with the OT ark of the covenant. (Disclaimer: this is based on a pastor's study, not mine... I can't translate Hebrew into Greek.)
4. The Church Father's commentary also found a parallel in John the Baptist leaping in the womb with David's dancing (leaping) before the ark.
And logically, the ark of the covenant carried the shekinah glory presence of the Lord in the OT time, and Mary carried the Lord in her womb.
"And the Word became flesh and dwelt (skaynay in Greek, shekinah in Hebrew) among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth." John 1:14