The Bible says all Christians are priests.
“be yourselves 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”. (1 Pet. 2:5,9).
So why do Catholics have only some people as priests?
Yes, Catholics believe in the common priesthood of all believers.
From the Catechism of the Catholic Church (para 1546)
Christ, high priest and unique mediator, has made of the Church "a 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.".
We are all part of the royal priesthood a holy nation, but we are not all ministerial priests. Only those who are chosen and called are ministerial priests. Ministerial priests are called by God to serve God and the people of God.
We find this in the Old Testament
"Then bring near to you Aaron your brother, and his sons with him, from among the people of Israel, to serve me as priests--Aaron and Aaron's sons, Nadab and Abihu, Eleazar and Ithamar.” (Ex 28:1).
Whilst God called some to serve him and his people as special priests he called all Israel to be a kingdom of priests and a holy nation
“Now therefore, if you will obey my voice and keep my covenant, you shall be my own possession among all peoples; for all the earth is mine, and you shall be to me a kingdom of priests and a holy nation.” (Ex 19:5-6)
Similarly whilst all Christians are part of the holy nation and a kingdom of priests, only some are called to be ministerial priests. As the Catechism explains (para 1547)
“…..the ministerial priesthood is at the service of the common priesthood. It is directed at the unfolding of the baptismal grace of all Christians. the ministerial priesthood is a means by which Christ unceasingly builds up and leads his Church.”
This is biblical:
“But on some points I have written to you very boldly by way of reminder, because of the grace given me by God to be a minister of Christ Jesus to the Gentiles in the priestly service of the gospel of God, so that the offering of the Gentiles may be acceptable, sanctified by the Holy Spirit.” (Rom 15:15-16).