Tim Staples explains this better than I could:
http://www.catholic.com/thisrock/2005/0503fea4.asp
"But even if a Protestant accepts the notion of Christians being priests and accepts the Catholic interpretation of 1 Timothy 2:5 and Hebrew 7:22–25 in this respect, this in no way shows that there is a distinct ordained priesthood apart from the universal priesthood of the faithful. First Peter 2 indicated that all Christians are priests—but not ministerial priests. Here was my biggest problem with the Catholic notion of a ministerial priesthood. The ordained ministers of the New Covenant are called apostles (cf. Eph. 4:11), elders (Jas. 5:14), bishops (1 Tim. 3:1), and deacons (1 Tim. 3:8ff). They are not referred to directly with the typical Greek word for "priest," which is hiereus. But the English word priest is derived from the Greek word presbuteros, or "elder." It does not originate from hiereus. The German word priester also has its origin from the Greek word for "elder." So there is etymological reason to say that the elder in the Christian Church was considered to be a priest. In fact, the Douay-Rheims Bible translates presbuteros as "priest," which can be a valid translation (see Jas. 5:14, DRV). Having said that, I must say that for me, it was not the word elder or priest that helped me to see the truth of the New Covenant priesthood; it was the function of the apostle, bishop, and elder, which is clearly revealed to be of a priestly nature. (A deacon is ordained, but he is not a ministerial priest.) There were basically four biblical steps I took on the road to discovering the New Covenant priesthood. First, I saw that although the standard noun for priest—hiereus—is not used for New Testament ministers, the verb form of hiereus is. And it is found when Paul refers specifically to his ministry as an apostle. He refers to his ministry as a "priestly service": "Because of the grace given me by God to be a minister of Christ Jesus to the Gentiles in the priestly service [Greek: hierourgounta] of the gospel of God" (Rom. 15:15–16). Second, I saw that 1 Peter 2:5–9 is a reference to Exodus 19:6: "and you shall be to me a kingdom of priests and a holy nation." This text indicates a universal priesthood in the Old Covenant. Yet in that same chapter, verse 22, we read: "And also let the priests who come near to the Lord consecrate themselves." I clearly saw that there was a universal priesthood in existence in the Old Covenant, but this did not exclude the possibility of a distinct ministerial priesthood as well. Could it be the same in the New Covenant? I discovered that it was. Third, as far as the term priest is concerned, it began to seem plausible to me that the Christians of the first century would avoid using it in naming the ministerial offices of the Church, because it was the same term being used by the more numerous Jewish and even pagan priests (cf. Luke 1:8–9; Acts 14:13). Christians used language to distinguish their priests from the Jewish and pagan priests of their day. But what was most important for me was the fourth step in the process. I saw in Scripture that New Covenant ministers functioned as priests. As the old saying goes: "If it walks like a duck and quacks like a duck. . . ."
Or would you like to argue against the Trinity because the word "trinity" isn't explicitely in the Bible either?