To belong to a parish is to belong to the Church, is to belong to Christ Jesus.
To belong to Christ is to belong to the Church, is to belong to a parish.
As stated in the Catechism of the Catholic Church (CCC)
759 The eternal Father, in accordance with the utterly gratuitous and mysterious design of his wisdom and goodness, created the whole universe and chose to raise up men to share in his own divine life… (CCC)
760 Christians of the first centuries said, “The world was created for the sake of the Church.” God created the world for the sake of communion with his divine life, a communion brought about by the “convocation” of men in Christ, and this “convocation” is the Church. Just as God’s will is creation and is called “the world,” so his intention is the salvation of men, and it is called “the Church.” (CCC)
And in the words of the U.S. Catholic Bishops
The parish is where the Church lives. Parishes are communities of faith, of action, and of hope. They are where the gospel is proclaimed and celebrated, where believers are formed and sent to renew the earth. Parishes are the home of the Christian community; they are the heart of our Church. Parishes are the place where God’s people meet Jesus in word and sacrament and come in touch with the source of the Church’s life. (U.S. Conference of Catholic Bishops 1993)
For a further explanation of why it is important to belong to a parish, learn more about how Catholics understand The Church.