The Church is catholic or universal because Christ established it to proclaim all of His teaching to all men, at all times, and in all places.
Jesus said, “Go into all the world and preach the gospel to the whole creation” (Mark 16:15). “But you shall receive power when the Holy Spirit has come upon you; and you shall be my witnesses in Jerusalem and in all Judea and Samaria and to the end of the earth” (Acts 1:8).
Jesus spoke of the growth of His Church when He gave us the parable of the mustard seed. “The kingdom of heaven is like a grain of mustard seed which a man took and sowed in his field; it is the smallest of all seeds, but when it has grown it is the greatest of shrubs and becomes a tree, so that the birds of the air come and make nests in its branches” (Matthew 13:31-32).