Why do you think the Church considers Mary to be the new Ark of the Covenant?

The Ark of the Covenant contained the "presence of God"; the tablets of the Mosaic law, the Ten Commandments, which is the word; it contained a pot with the mana God provided, which is the bread; it contained the rod of Aaron, the high priest. These three items represent the presence of God and these are also the three titles by which Jesus is known: he is "the Word made flesh" (Jn. 1), the "Bread of life" (Jn. 6) (born in the town of Bethlehem, which in Hebrew means "house of bread") and the "High Priest according to the line of Melchiz'edek (Heb. 5). Mary mirrored exactly this when she carried Jesus in her womb - as a "new Ark", or as we view it today, as a living Tabernacle.

Of interesting note is that this is made visible in Scripture, yet it is partially hidden at the same time because of the way we read it. When the books of the Bible were written they did not have chapter and verse. It wasn't until 1227 a.d. when Stephen Langton divided each of the books of the Bible into chapter and verse. When we read the book of Revelation we are all familiar with the beginning of chapter 12 where we see a direct and vivid reference to our Blessed Mother. If we take it back a few verses, which we do on the Feast of the Assumption, we read, "Then God's temple in the heavens was opened, and the ark of his covenant was seen within his temple; and there were flashes of lightning, loud noises, peals of thunder, an earthquake, and heavy hail. And a great sign appeared in heaven, a woman clothed with the sun, with the moon under her feet, and on her head a crown of twelve stars; she was with child and she cried out in her pangs of birth, in anguish for delivery". Read together, without the chapter and verse division we have a clear image from Scripture that Mary is indeed seen as the new ark of the covenant. Also important to note about this is that even though the division of chapter and verse is recognized universally, it is not understood that the separation is "inspired" as Scripture is inspired and as such has no impact on the understanding of Scripture. It is interesting that Stephen Langton separated chapters at that point in the middle of the "seventh trumpet" message and not at the end of that.

The Ark of the Covenant carried God's Word; the womb of the Blessed Virgin Mary carried God Himself - the Word of God made flesh.