The answer, while not popular or politically correct, is that he is exactly the one to judge! His role as the leader of the Roman Catholic Church, is to know the Word of God, to teach the Word of God, and to discipline those within his flock who fail to live according to the Word of God! It is true that Jesus made the statement, "Judge not, that ye be not judged" (Mt. 7:1). However, He also said, "Judge not according to the appearance, but judge righteous judgment" (Jn. 7:24).
So, why the difference? Context, it is all about context. His statement recorded in Matthew 7:1 is followed by "For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again" (7:2). In other words, be careful not to hold others to a standard you are not willing to live up to yourselves.
The Apostle Paul, writing to the Church at Corinth, rebuked the leaders for failing to deal with "sin in the camp." In 1 Corinthians 5:1-13, it is clear that those who profess faith in Christ, are to live according to the teachings of God's Word; when they fail to do so, they are to be confronted, and unless they repent, they are to be "shunned" by the congregation! Ironically, the sin mentioned in the chapter is a sexual sin.
The Word of God is the standard we are to use to determine the appropriateness of behavior. We are to use that standard because it is the standard He will use when He judges mankind on Judgment Day (Jn. 12:48; Rom. 2:12; etc.). Even Pilate (Jn. 18:31), and Ananias, the Chief Priest (Acts 24:1-6), understood the Word of God is the basis for righteous judgment! Paul said, in 1 Corinthians 6:3,
"Know ye not that we shall judge angels?
How much more things that pertain to this life?"