Thanks for the questions.
- Since Jesus was a Jew, why are we Catholic?
These paragraphs from the Catechism appear to answer most of your first question:
The Good News: God has sent his Son
422 But when the time had fully come, God sent forth his Son, born of a woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. (Galatians 4:4-5)
This is the gospel of Jesus Christ, the Son of God: (Mark 1:1) God has visited his people. He has fulfilled the promise he made to Abraham and his descendants. He acted far beyond all expectation - he has sent his own 'beloved Son'. (Mark 1:11; cf. Luke 1:5, 68)
423 We believe and confess that Jesus of Nazareth, born a Jew of a daughter of Israel at Bethlehem at the time of King Herod the Great and the emperor Caesar Augustus, a carpenter by trade, who died crucified in Jerusalem under the procurator Pontius Pilate during the reign of the emperor Tiberius, is the eternal Son of God made man. He came from God, (John 13:3) descended from heaven, (John 3:13; 6:33) and came in the flesh. (1 John 4:2) For the Word became flesh and dwelt among us, full of grace and truth; we have beheld his glory, glory as of the only Son from the Father. . . And from his fullness have we all received, grace upon grace. (John 1:14,16)
424 Moved by the grace of the Holy Spirit and drawn by the Father, we believe in Jesus and confess: You are the Christ, the Son of the living God. (Matthew 16:16)
On the rock of this faith confessed by St. Peter, Christ built his Church.
(cf. Matthew 16:18; St. Leo the Great, ( A.D. c.391 - 461), Sermo 4,3:PL 54,150-152; 51,1:PL 54,309B; 62,2:PL 54,350-351; 83,3:PL 54,431-432)
Jesus did not abolish the Law given by God to Moses on Mount Sinai but he fulfilled it by giving it its definitive interpretation. He himself was the divine Legislator who fully carried out this Law. Furthermore, as the faithful Servant, he offered by means of his expiatory death the only sacrifice capable of making atonement for all the transgressions committed by men under the first Covenant.
In doing so, He retained certain critical teachings of Judaism like the Ten Commandments He also brought His Gospel teachings to the world.
These teachings together with those from the Old Testament make up the Christian faith.
Now you may ask:
- If the rock of this faith confessed by St. Peter referred to in paragraph 424 is the Christian faith, why do we call ourselves Catholic?
Well, in the early Church there was a problem similar to what we have today. Many congregations were calling themselves Christian but were not officially following all the Teachings Jesus wanted them to follow.
St. Pacian of Barcelona tells us in the 4th century:
Suppose I entered, this very day, into a populous city, and found there Marcionites, Apollinarists, Cataphrygians, Novatians, and others of the same sort, all calling themselves Christians.
- By what name should I be able to recognize the congregation of my own people, were it not from its being called Catholic?
The word Catholic does mean universal but it also means the Christian faith according to its totality, meaning a faithful Catholic is believing everything Jesus wants them to believe.
He also said:
This name Catholic sounds not of Marcion, nor of Apelles, nor of Montanus, nor does it take heretics as its authors. . . . . Christian is my name, but Catholic my surname. That names me, this describes me; by this I am approved; by that designated.
And if at last we must give an account of the word Catholic, and express it, from the Greek, by a Latin interpretation, Catholic is everywhere one, or, as the more learned think, obedience in all the commandments of God.
Therefore he who is a Catholic, the same is obedient to what is right. He who is obedient, the same is a Christian, and thus the Catholic is a Christian.
Also if the Pope is infallible, why was St. Peter (our first pope) rebuked by the Apostle Paul in Galatians 2?
Peter was rebuked because of his bad behavior. The pope is a mere man just like you and me. He goes to Confession for his sins just as St. Peter and Paul did. Many Protestants bring up Galatians 2 to try to proof Peter is not infallible but they don’t understand infallibility.
Infallibility means that the Pope will be protected from officially teaching error in areas of faith and morals as it relates to Christian Teachings. It doesn't mean he will always say the most holiness thing(s) or do the most holiness thing(s). It is a negative safeguard.
Read this posting for more:
This posting will also help you understand the issue:
Finally, we all know that St. Peter was married (Matthew 8:14), so my question is, did he divorce his wife? (Matthew 19:29)
- Why would you take two distinct passages out of context that are 11 chapters apart and erroneously conclude St. Peter divorced his wife?
Faithful Catholics do not take bible passages out of context . . . most of the time. Protestants are more likely to do this to prove their erroneous point.
I hope this helps,