Are all Christians priests? (cf. 1 Pt. 2:5,9)

Once more, we will try to establish the case for the catholicity of the Holy Bible by answering the queries of our non-Catholic friends.

Here is another question regarding the biblical portrait of Christian priesthood:

If the Bible is a Catholic book...
Why does it show that all Christians are priests? (1 Pet. 2:5,9)

MY REPLY: Well, the Catholic Church also acknowledge the priesthood of every baptized Christians.

Christ, high priest and unique mediator, has made of the Church’s kingdom, priests for his God and Father. The whole community of believers is, as such, priestly. The faithful exercise their baptismal priesthood through their participation, each according to his own vocation, in Christ’s mission as priest, prophet and king. Through the sacraments of Baptism and Confirmation the faithful are consecrated to be … a holy priesthood. 

CCC # 1546 (emphasis added)

As a matter of fact, a lot of typological evidences has been written to affirm the catholic belief of "priesthood." The passage from the first epistle of St. Peter gives us only an insight to the fullness of truth regarding the subject matter. 

1 Peter 2:5, 9 NRSVCE
like living stones, let yourselves be built into a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ. 

But you are a chosen race, a royal priesthood, a holy nation, God’s own people, in order that you may proclaim the mighty acts of him who called you out of darkness into his marvelous light.

As we all know, Catholics have the unique way to see the New Testament as the fulfilment of the Old Testament.

The New Testament is in the Old concealed, the Old is in the New revealed.
-Anonymous

With regards to the "priesthood," the Holy Bible tells us that it is a divine office instituted by God himself.

In the Old Testament, we can find three types of priesthood ordered by God.

(1). High Priest – Aaron (Ex. 28:1)
(2). Ministerial Priests – Aaron’s sons (Ex. 19:6; 28:1)
(3). Universal Priests – Israel (Ex. 19:6). 

Interestingly, New Testament also proclaims "new" priesthood patterned to the old.

(1) High Priest – Jesus Christ (Heb. 3:1)
(2) Ministerial Priests – the ordained bishops and priests (Rom. 15:16; 1 Tim. 3:1,8; 5:17; Titus 1:7)
(3) Universal Priests - all the baptized (1 Pet. 2:5,9; Rev. 1:6)

CONCLUSION: The Bible affirms catholic belief of the three types of priesthood ergo once again, the Bible is indeed a Catholic Book. :)